Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 24° 23'. He then
Drives 1 mile (1 mile = 5280 ft)more and measures the angle of elevation to be 33° 12'. Find the
Height of the mountain to the nearest foot.

Question

Quizplus · Accepted Answer

Using trigonometry, we can solve this problem by setting up equations based on the tangent of the angles given, which is the ratio of the opposite side (height of the mountain, h) to the adjacent side (distance from the mountain). Let x be the distance from the mountain when the first angle was measured. Then, the tangent of the angles gives us two equations:1. tan(24° 23') = h / x2. tan(33° 12') = h / (x - 5280)Solving these equations simultaneously allows us to find the value of h, the height of the mountain. After calculating, the height of the mountain rounds to 7787 feet.

Bob Is Driving Along a Straight and Level Road Straight