Question

A plane flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 35,000 feet. The pilot would like to estimate her distance from the Gateway Arch. She finds that the angle of depression to a point on the ground below the arch is 22◦ . What is the distance between the plane and the arch?

Answer 1

Answer:

93,431.4 feet.

Step-by-step explanation:

Let x represent distance between the plane and the arch.

We have been given that a plane flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 35,000 feet. The pilot finds that the angle of depression to a point on the ground below the arch is 22◦.

We can see from our attachment that plane, the gateway arch and angle of depression forms a right triangle with respect of ground.

The side with 35,000 ft is opposite side and side x is hypotenuse for 22 degree angle.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{sin}(22^{\circ})=\frac{35,000}{x}$

$x=\frac{35,000}{\text{sin}(22^{\circ})}$

$x=\frac{35,000}{0.374606593416}$

$x=93,431.350689$

$x\approx 93,431.4$

Therefore, the distance between the plane and arc is 93,431.4 feet.