PHYSICAL GEOGRAPHY LAB 121 Y O U R N A M E __________________________ Cliffe, Matherly, Curran, Therkalsen, Goodman 50 POINTS POSSIBLE Grossmont College Use Pencil Only EXTRA CREDIT on back pages! LAB #2: THE GEOGRAPHIC GRID William Blake’s “Newton” is not really a picture of an individual. Instead, it dramatizes and glorifies the detached, and almost God-like scientist who can solve the mysteries of the universe and display the results with mathematical precision. [The Tate Gallery, London, England] 2 Right-Triangles and “SOHCAHTOA” A. HEIGHT-OF-OBJECTS 1. Determine “Flagpole Height:” (+2 Points) (a) Relative to  , correctly label the diagram above using opp, adj, and hyp. (b) Using a compass protractor (get one from your instructor), measure angle  directly from the diagram above:  = _______________ (c) Given both  and the “horizontal distance” of 50 [ft]: (1) Which trig function can be used to determine “flagpole height?” ______ (2) Using “SOHCAHTOA,” write the “equation” for this trig function: ______________________________ (d) Use the space below and your calculator to determine “flagpole height” (show all work and units): Flagpole Height = ___________________ (to nearest foot) 2. Determine “Tree Height:” (+2 Points) (a) You have a tape measure and a clinometer (a device that measures angles). Explain in clear, complete sentences how to easily measure the height of the tree pictured above. (Unlike in the last question, there’s nothing here to measure…Just explain.) (b) Moving closer or farther from the tree does not change your answer; why not? (i.e., if “horizontal distance” changes, what variable compensates?) 3 “Gunsight View” Used to aim at the object-of-interest B. USING A “CLINOMETER” TO SET Rotate the Compass-Housing until the “W” (270o) lines-up to the white Triangular Pointer (which is located on the Hinge). Mirror Used to see your Clinometer Arrow TO USE Ignore the Compass Needle. Instead, use only the tiny arrow of the Clinometer. Photo by: Andy Warhol “TRIANGULAR POINTER” Note: 2o Interval between tic-marks The Clinometer’s Arrow will point to 0o when held level-to-thehorizon (as shown). From SOHCAHTOA: 4 tan  = Measuring Height-of-Objects To set your Compass for use as a Clinometer  Align W (270o) to the white “triangular pointer” (+4 Points) 1. Top of Light Pole (Use a Light Pole on the West Side of the Lab Building):  Horizontal Distance from Pole, in feet (tape measure) = _____________________ (Do so in a direction that is level, or that is as close to level as possible)  Angle to Top of Light Pole (clinometer) = _____________________  Compute Height (add #’s to diagram; then show all work, round to nearest foot; prominently circle your answer): You ! Angle = _______ Light Pole tan = opp adj Distance (Tape Measure) = _____________ 2. Science Lab Building (The top of the 2nd Floor Roof): (+4 Points) Note: Measure horizontal distance to the edge of the Rooftop “Overhang” (not to the wall of the 1st Story).  Horizontal Distance from Rooftop “Overhang,” in feet (tape measure) = _____________  Angle to Top of Rooftop “Overhang” (clinometer) = ________________________  Compute Height (draw diagram and show all work, rounded to nearest foot; prominently circle your answer): 5 C. LATITUDE/LONGITUDE SYSTEM: The Globe 1. Use a dashed line to sketch-in the following Parallels of Latitude. Label each using the correct number from the Latitude System. (If not visible on the diagram, then write “not visible.”) o a) 35 N o b) 10 S c) Tropic of Capricorn d) Arctic Circle e) North Pole f) South Pole +2 Points Incorrect Responses = -1/2 6 2. Use a dashed line to sketch-in and label the following Meridians of Longitude (using the appropriate name, not the letter; note that all are visible): o a) 10 W +2 Points Incorrect Responses = -1/2 o b) 20 E o c) 58 W o d) 145 W e) Prime Meridian f) International Dateline 3. On the globe below: (a) Quickly darken and label the Equator, Prime Meridian, and Int’l Dateline. (b) Then, draw a small “X” at the following locations, labeling each with the appropriate letter (a-d): o o o o a) 35 N , 90 W b) 20 N , 30 E o o o o c) 25 S , 32 W d) 15 S , 20 E +3 Points Incorrect Responses = -1/2 7 D. LATITUDE/LONGITUDE SYSTEM: In Map View The following grids (located on this page and the next) represent portions of the Earth’s Latitude/Longitude System as portrayed in “map view.” For each, do the following: 1. Fully label each line on each of the following two Map Grids with the correct latitude or longitude, relative to the “Grid Interval” given at the bottom of the map.(Check your labeling against a Globe or a classroom wall-map, especially for the lines of Longitude.) o 2. Darken-in any grid-lines that have an alternative name in English (e.g., 0 Lat = Equator); appropriately include that name on the map. 3. Write the latitude/longitude for each of the following locations, as found on the maps: MAP GRID I +3 Points (1) ________________________ (8) ________________________ 150OE 130OW 1 2 4 7 10ON 6 5 3 8 GRID INTERVAL = 10O Confirm that you looked at a Globe, and that your Lines of Longitude are correctly labeled: YOUR INITIALS _________ 8 MAP GRID II +3 Points (GRID INTERVAL = 5O, not 10O) 10) ________________________ 14) ________________________ 75OE 18 11 10 17 13 12 14 20ON 15 16 GRID INTERVAL = 5O Did you correctly and fully label each Grid Line? Yes _____ No _____ Didn’t Check ______ 9 E. FINDING LATITUDE and LONGITUDE Completely Incorrect Responses = -1/2 Use either the Globes or the Wall-Maps in the classroom. Work fast…if there’s a question that takes you more than 5 seconds to figure out, then ask somebody immediately for help! Big Globe: (+2 Points) Pearl Harbor, Hawaii lat. _______ Cabo San Lucas (Tropic of Cancer) lat. _______ Be accurate: Some of these Lat/Long’s will be used on Exam #1 Cape Town, South Africa long. _______ long. _______ lat. _______ long. _______ U.S. Map (on side wall) - Name the closest major U.S. city, and its NFL football team: (+3 Points) 32½oN Lat, 117oW Long 38½oN Lat, 94½oW Long 40¾oN Lat, 80oW Long city = _________________ team = _____________ city = _________________ team = _____________ city = _________________ team = _____________ From San Diego, in what “cardinal direction” (E, SE, SSW, etc.) is Las Vegas (Nevada) located? Las Vegas is located to the __________________ World or European Map: Be accurate: Some of (+2 Points) these Lat/Long’s will be used on Exam #1 London, England Baghdad, Iraq Moscow, Russia lat. _______ lat. _______ lat. _______ long. _______ long. _______ long. _______ California Map: Los Angeles lat. ____________ long. ____________ Reno, Nevada lat. ____________ long. ____________ (+2 Points) Don’t pick the wrong city ! Be sure you really measured by 1½ o! So put the side of this page up against the boundary of the map and “mark off” 1½ o of Lat; then, lay one mark onto the map at San Diego and see how far the other mark extends straight-up north…there’s your city! Which is farther west, Los Angeles or Reno? ______________________ (This is Johnny Carson’s classic question from the Tonight Show) Circle the city that is most-exactly due-north of San Diego by ~1½ o of Latitude: Temecula Barstow Palm Springs Los Angeles San Bernadino Medium-size Globes (on side tables): (+1 Point) Start at Madrid, Spain. Go west 120o. Name the city: ________________________ (Starts with an “E,” as labeled on the medium-sized globes) 10 F. 7 ½‘ QUAD MAPS (La Mesa Quad) Use your own personal La Mesa Quad Questions start on the next page C P D o 32 47’ 30” N o 32 ___ ___ N o 32 ___ ___ N o 32 ___ ___ N o 32 ___ ___ N o 32 45’ 00” N B A 11 (+3 Points) On your La Mesa Quad: (a) On the Eastern Boundary of your La Mesa Quad: Prominently circle-withpencil the four printed labels for Latitude (Note: Most numbers on the side of the map are not part of the Latitude/Longitude System…be careful to circle the correct four printed labels!) (These include: 32o 45’ 00”, 32o 47’ 30”, 32o 50’ 00”, and 32o 52’ 30”) You probably already did some of this with your instructor during the Briefing (b) On the Southern Boundary of your La Mesa Quad: Prominently circle-withpencil the four printed labels for Longitude (Note: Most numbers on the side of the map are not part of the Latitude/Longitude System…be careful to circle the correct four printed labels!) (These include: 117o 00’ 00”, 117o 02’ 30”, 117o 05’ 00”, and 117o 07’ 30”) (c) Have your instructor confirm (in the box) that you’ve circled the correct labels: (Once initialed by your instructor, then highlight all 8 printed Lat/Long’s on your map with a highlighter) (d) The northern boundary of the La Mesa Quad is a line that runs in the east-west direction. Thus, this line represents an arc of: _____________ (Latitude or Longitude?) How far north-of-the-Equator is this arc located? (answer in angular measure using degrees, minutes, and seconds) _______________________________ (Answer is printed on sides of map’s N boundary) (+3 Points) On the previous page, assume the map represents the La Mesa Quad: (a) On the previous page, complete the proper labeling of the Latitude and Longitude “crossed tic-marks (+)” found at locations A, B, C, and D so that they correctly reflect the La Mesa Quad. Include Degrees, Minutes, and Seconds for all four. Also correctly include N or W. Note: On the sides of USGS Quad maps, a 2½ minute Interval is used between successive tics. (b) Four “crossed tic-marks (+)” are drawn within-the-map on the last page (as is also the case on your actual La Mesa Quad); of the four, name the “crossed tic-mark (+)” that is labeled “P” Latitude = ____________________ Longitude = _____________________ (c) At the bottom of the western border of the map, find the line that’s drawn with extra tic-marks (it’s found between 32o 45’ 00” N and 32o 47’ 30” N). This line extends only 2½ minutes. Furthermore, it’s broken into 5 smaller intervals of 30” (or ½’) each (that is: 5 x ½’ = 2½’). On this line, label each tic-mark (using degrees, minutes, and seconds). (+3 Points) Now, go back to your actual La Mesa Quad: (a) Find Lake Murray’s Latitude and Longitude (Include minutes and seconds): Use the “crossed tic-mark (+)” near the lake’s northern “finger,” and highlight it. Latitude = _________________________ Longitude = __________________________ (b) Name the High School that is located at 32o 45’ 15” N Lat, 117o 2’ 20” W Long: _______________________ (c) Name the college that is located at 32o 48’ 50” N Lat, 117o 0’ 20” W Long: ________________________ Where needed on pages 8 and 9, do your answers include N, S, E, or W? Yes _____ No _____ 12 G. CONVERSIONS Use your Latitudes from above; round to nearest mile 1. Show all work and show all units through all computations. (Use the format presented in Lab #1. Don’t show “scratch” in the body of your work. Either do scratch in-the-margins or on “scratch paper.”) o Going N-to-S along an Arc-of-Longitude…Convert Latitude to Miles: (+3 Points) o a. How far is San Diego (_____ latitude) in miles from the Equator? b. How far is London (_____o latitude) in miles from the Equator? c. How far is Cape Town (_____o latitude) in miles from the Equator? 2. Going W-to-E along an Arc-of-Latitude…Convert o Longitude to Miles: (+3 Points) a. Review: 1o Longitude is equal to how many miles at Earth’s surface (i.e., write the Equation that converts oLongitude into miles)? 1o Longitude = b. How far is Dallas, Texas (33o N Lat, 97oW Long) from San Diego (33oN Lat, 117oW Long) in miles? 1) Determine the “longitudinal separation” between Dallas vs. San Diego (i.e., how far apart?): 2) What’s the shared latitude of the two places? ____________________ 3) Properly set-up the conversion (as in LAB #1), then solve. (Show work and all units.) c. How far offshore are the Galapagos Islands (0o Lat, 90oW Long) from the coast of Ecuador (0o Lat, 80oW Long) in miles? 1) How far longitudinally is the Galapagos from Ecuador’s coast? ________________ 2) What specific latitude must be used in your Conversion Factor? ___________________ 3) Properly set-up the problem as done in LAB #1 by showing the “given quantity” multiplied by the correct “conversion factor”(make sure to put oLong in the denominator). Then solve. (Show work and all units.) +8 POINTS POSSIBLE 13 of "Extra Credit" H. EXTRA CREDIT: Right Triangles (and “SOHCAHTOA”) To answer the following, use the “trig identities” for sin, cos, and tan, as expressed by “SOHCAHTOA.” . NOTE: Make sure your calculator is set for DEGREES, not for RAD (radians). Do so by hitting the MODE button, then highlighting the word DEGREES. 1. Right Triangle circumscribed within Earth (angle  ) (+1 Point) a. Relative to angle  , correctly label the diagram by writing the terms opp, adj, and hyp (opposite, adjacent, hypotenuse) b. Assume:  = latitude of Pearl Harbor. (From above, or from a Globe, or from an Atlas: Pearl’s Lat = ________) Using your calculator’s trig buttons, make the following simple calculations:  Equator sin  = ___________ cos  = ___________ 2. Right Triangle circumscribed within Earth (angle  ) (+1 Point) a. Relative to angle  , correctly label the diagram by writing the terms opp, adj, and hyp. b. Assume:  = latitude of London. (From above, or from a Globe, or from an Atlas: London’s Lat = ________) Using your calculator’s trig buttons, make the following simple calculations: sin  = ___________ cos  = ___________  Equator 14 3. Latitudinal Variation (in sin, cos, and thus in Solar Energy Receipt) a) Trig Functions - Using a calculator, compute the following, both as a decimal (rounded to hundredths) and as a percent (i.e., decimal x 100, rounded to tenths): (+1½ Points) decimal sin (Equator) percent = ________ _________ sin (North Pole) = ________ Round to hundredths _________ decimal percent cos (Equator) = ________ _________ cos (North Pole) = ________ _________ Round to hundredths Round to tenths Which is minimized as one moves poleward, sin or cos of latitude? Round to tenths ________ Which is minimized as one moves equatorward, sin or cos of latitude? ________ Thus, since Solar Energy Receipt generally decreases poleward, then Sunshine Receipt varies latitudinally as a function of which, sin or cos? _______ b) Intensity of Incoming Solar Radiation (“Insolation”) (+1½ Points) OUR REASONING: On a given day, assume that noontime Solar Radiation is mostintensely received at the Equator (i.e., is 100% at the Equator). Thus on that day, Solar Radiation will be less-intensely received when moving away from the Equator. Hence, since the cos also decreases with an increase in angle, the intensity of Solar Radiation will vary as a function of the cos of Latitude. YOUR TASK: Compute the intensity of incoming Solar Radiation as received at other latitudes using the cosine trig function. (You only need to complete The Table; 0 o and 45o are already done as examples. The diagram on the right simply shows the situation at 0o, 30oN, and 60oN.) Latitude cos (LAT) percent 90o ______ _____% 75o ______ _____% 60o ______ _____% 45o 0.709 30o ______ _____% 15o ______ _____% 0o 1.000 100_% ? ? 71_% 100% 15 4. Drawing Right Triangles circumscribed in Earth a) The sin of Latitude (+1½ Points) 1. Review: Properly label the sides of this Right Triangle relative to angle  . Then properly define sin  (as per SOHCAHTOA). sin = ------------ 2. On the diagrams below, draw a Right Triangle circumscribed in Earth relative to latitudes “a” then “b” then “c.” Then, highlight the “opp” side for each. c b a Equator Equator Equator 3. What happens to the “opposite” side as one heads poleward? ________________ increases or decreases? 4. Thus (if one increases the “opposite” side and thus increases the numerator of the fraction), what has to happen to sin(LAT) as one moves poleward? ___________________ increases or decreases? 5. Result: Many things that increase with latitude (e.g., the Coriolis Effect is nonexistent at the Equator, but maximized at the Poles) vary as a function of the _______ of latitude? sin or cos? 16 b) The cos of Latitude (+1½ Points) 1. Review: Properly label the sides of this Right Triangle relative to angle  . Then properly define cos  (as per SOHCAHTOA). cos  = ------------ 2. On the diagrams below, draw a Right Triangle circumscribed in Earth relative to latitudes “a” then “b” then “c.” Then, highlight the “adj” side for each. c b a Equator Equator Equator 3. What happens to the “adjacent” side as one heads poleward? _______________ increases or decreases? 4. Thus (if one decreases the “adjacent” side and thus decreases the numerator of the fraction), what has to happen to cos(LAT) as one moves poleward? ___________________ increases or decreases? 5. Result: Many things that decrease with latitude (e.g., the intensity of Sunshine Receipt, which generally decreases poleward) vary as a function of the ________ of latitude? sin or cos?
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