What is the height of the mountain?

Question

A car was driving toward a high mountain straight ahead. The driver could see the top of mountain with the angle of elevation 38 degrees. After driving 1850 ft, the drive is looking at the top of the mountain at the angle of elevation 43.5 degrees. Find the height of the mountain.

Answer 1

let h= height of the mountain, x = distance from 2nd position to the bottom of the mountain

1850+x = distance from the 1st position to the bottom of the mountain

construct 2 right triangles. 1st has angle 38 and base 1850+x. 2nd has angle 43.5 and base x

tan38 = h/(1850+x)

tan43.5 = h/x

h=(1850+x)tan38

h= xtan43.5

xtan43.5 = 1850tan38 + xtan38

x(tan43.5-tan38) = 1850tan38

x = 1850tan38/(tan43.5 -tan38)

h=xtan43.5 = tan43.5(1850tan38)/(tan43.5-tan38)

tan43.5 = about .949

tan38 = about .781

h=about .949(1850).781/(.949-.781)

h= about 1371.16/.168 =

mountain = about 8161.7 feet high