In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive 13 miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.Round your answer to two decimal places.
A) 51.64 miles
B) 8.18 miles
C) 1.58 miles
D) 1.30 miles
E) 16.36 miles

Question

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive 13 miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.Round your answer to two decimal places. ​  ​  ​
A) 51.64 miles 
B) 8.18 miles 
C) 1.58 miles 
D) 1.30 miles 
E) 16.36 miles

Quizplus · Accepted Answer

Let 'h' be the height of the mountain and 'd' be the distance between the observer and the mountain. Then from the given data, we can form the following equations:
h/d = tan 3.5°
h/(d - 13) = tan 9°
Using the first equation, we can express 'h' in terms of 'd':
h = d*tan 3.5°
Substituting this value of 'h' in the second equation and simplifying, we get:
d^2 - (d - 13)^2 = (h/tan 9°)^2
Solving for 'd', we get d = 1.30 miles (rounded to two decimal places). 
Substituting this value of 'd' in the equation for 'h', we get h = 0.25 miles or approximately 1320 feet. Hence, the best choice is D, 1.30 miles.

In Traveling Across Flat Land,you Notice a Mountain Directly in Front