HELP PLEASE!! Planes that fly at high speeds and low elevations have radar systems that can determine the range of an obstacle and the angle of elevation to the top of the obstacle. The radar of a plane flying at an altitude of 20,000 feet detects a tower that is 25,000 feet away, with an angle of elevation of 1∘.

a. How many feet must the plane rise to pass over the tower?

The plane must rise at least _feet to pass over the tower.

Question 2
b. Planes cannot come closer than 1000 feet vertically to any object. At what altitude must the plane fly in order to pass over the tower?

The plane must fly at an altitude of at least _ feet to pass over the tower.

a. About 436 ft

b. 21,436 feet

Step-by-step explanation:

a. Notice how the plane's rise (h), its horizontal distance from the tower, and its distance to the top of the tower (25,000 ft) all form a right triangle. If we want to find h, we need some way of putting it in an equation with the two quantities we already know: the angle of elevation and the distance to the top.

In the language of right triangles, we want to combine an angle, the side opposite the angle, and the hypotenuse. The sine function is perfect for this, since . For our problem, opp = h, hyp = 25,000, and θ = 1°, so our equation becomes

or equivalently

ft (rounded up to the nearest whole foot)

b. If the plane is currently flying at 20,000 feet, it needs to rise about 436 feet to clear the top of the tower, and another 1,000 feet to follow safety protocol, making its required altitude 20,000 + 1,000 + 436 = 21,436 feet.

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step-by-step explanation: