Trigonometry Assignment 2

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A ladder is leaning up against a 10-foot wall at an angle of elevation of 65°. How far is the foot of the ladder from the wall? Round your answer to the nearest tenth of a foot

Oct 14th, 2014

NOTE:  For a right triangle:

              sin A = opposite/hypotenuse

               cos A = adjacent/hypotenuse

               tan A = opposite/adjacent

                      (Where 'A' represents your angle value)

               Whatever two sides are labeled, use its proper corresponding formula.

We are finding the length of the foot of the ladder to the wall.  We can let 'x' represent this concept.

You may need to draw a shape picture to represent your given story problem.  If done correctly, it should look something like in the following link:     Wall&LadderShapeImage.png

According to this image, our given angle is 65 degrees (A = 65), the angle's opposite side is 10 feet (opposite = 10) and the angle's adjacent side is x  (adjacent = x).  Since the opposite and adjacent sides are labeled, we can use the 'tan' formula to find our solution.  Be sure to round your result to the nearest whole number.

                        tan A = opposite/adjacent                 <Tan formula>

                        tan 65 = 10/x                                     <Substitute>

                    x*(tan 65) = (10/x)*x                             <Multiply both sides by the fraction denominator, which is x>

                   x*(tan 65) = 10

                  x*(tan 65) = 10                                       <Divide both sides by tan 65>

                   /(tan 65)        /(tan 65)

                        x = 10 / (tan 65)

                        x = 10 / 2.144506921                     <Use a calculator to evaluate tan 65>

                        x = 4.66307658                              <Divide>

                       x = 5                                               <Round to the nearest whole number.>

SOLUTION:  The foot of the ladder is approximately 5 feet from the wall.

Oct 14th, 2014

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