Question

A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 30000 feet. The pilot would like to estimate her distance from Gateway Arch. She finds that the angle of depression to a point on the ground at the arch is 23°. Find the distance between the plane and the arch. Round your answer to the nearest foot. (Do not include ft in your answer)

Answer 1

Answer: 70676

Step-by-step explanation:

First we draw a diagram representing the problem, which can be found in the picture uploaded,

Point a is the point of the plane, you can see where the angle of depression is imputed in the diagram, point C is the point where the gateway arch is, and drawing a vertical line to the ground from the point of the plane, point Blank is where that vertical line touches the ground

So we can tell the the angle of depression from the plane to the arch is the same as the angel of elevation from the arch to the plane

And we are to look for the distance between B and C which is labeled x in the diagram

So looking at the right angle triangle made from this question, we can see we have the opposite length which the angle of elevation from the arch is looking at, and we are looking for the adjacent length, so we use SOH, CAH, TOA, to solve

Choosing TOA which means

Tan(angle) = (opposite length)/(adjacent length)

Tan 23 = 30000/x

Multiplying both sides by x

xtan23 = 30000

Dividing both sides by tan23

x = 30000/tan23

x = 70675.57

Approximately 70676