Trigonometry Triangles

Mathematics
Tutor: None Selected Time limit: 1 Day

1.       A mountain is due north and the peak is 20° above the horizon (the angle between a level line drawn straight north and a line drawn to point at the peak is 20°). You walk 1000 feet due east and the mountain is now 10° west of north (you have to rotate 10° counterclockwise from facing north to be facing the peak). How tall is the mountain? Note that the ground is level as you walk east and we are assuming the earth is flat.

Sep 23rd, 2015

Hello!

Denote the initial horizontal distance to the mountain as x and its height as h. Then

h/x = tan(20°) or h=x*tan(20°).

From the horizontal movement

1000ft/x = tan(10°) or x=1000ft/tan(10°).

The final formula is

h=1000ft * tan(20°)/tan(10°).

Use calculator and obtain

h = approx 2064ft.

Please ask if something is unclear.
Sep 23rd, 2015

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Sep 23rd, 2015
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