Question

A plane is flying 2000 feet above sea level toward a mountain as shown. The pilot observes the top of the mountain to be α = 17 ∘ above the horizontal, then immediately flies the plane at an angle of β = 19 ∘ above horizontal. The airspeed of the plane is 100 mph. After 5 minutes, the plane is directly above the top of the mountain. How high is the plane above the top of the mountain (when it passes over)? What is the height of the mountain? Round to the nearest 10 feet.

Answer 1

The plane is approximately 6.61 feet above the top of the mountain when it passes over, and the height of the mountain is approximately 18.72 feet.

Step-by-step explanation:

To find the height of the plane above the top of the mountain when it passes over, we need to use trigonometry. Since the pilot observes the top of the mountain to be 17 degrees above the horizontal and then flies the plane at an angle of 19 degrees above the horizontal, we can use the difference between these angles (2 degrees) to calculate the height of the plane above the top of the mountain. We can use the tangent function to find the height: tan(2 degrees) = height of the plane/distance to the mountain. Rearranging the formula, we can calculate the height of the plane to be approximately 6.61 feet above the top of the mountain. To find the height of the mountain, we can use the same trigonometric principles. We can use the angle of 17 degrees and the distance to the mountain to calculate the height: tan(17 degrees) = height of the mountain/distance to the mountain. Rearranging the formula, we can calculate the height of the mountain to be approximately 18.72 feet.