Question

In traveling across level ground, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 4.5o . After you drive 10 miles closer to the mountain, the angle of elevation is 12o . Approximate the height of the mountain.

Answer 1

1.25 miles

Explanation:

Check the image i uploaded.

You can form a right triangle with base b, height h ( the height of the mountain) and angle 12

for that one we can write

tan 12=h/b

for the triangle that has base 10+b, height h and angle 4.5 we write

tan 4.5= h/(10+b)

then we can solve both for h and equate

tan (12) *b= tan (4.5) (10+b)

solving for b you get b=5.88 miles. (remember to calculate trigonometric functions use a scienfitic calculator and be careful it is correclty set in degrees in this case)

Once you have b you can use any of the equations to calculate h

i'll use tan (12)*b=h=1.25 miles.