A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 40,000 ft. (description)

Question

A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 40,000 ft. 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 25°. (Round your answers to the nearest foot.)

a. What is the distance between the plane and the base of the arch?

b. What is the distance between a point on the ground directly below the plane and the base of the arch?

I am really struggling with this portion of my homework. If someone could show me how to solve this step by step and give the correct answer at the end it would help me greatly on the rest of this assignment. Thank you!

Answer 1

It sounds like you want side "c".

Given: a=40000

α=25°

γ=90°

a/sinα=b/sinβ=c (sin90=1)

180-25-90=65°=β

40000/.4226.......=946,480.......'=c

B) you want side "b".

Figure it like I did side "c". See the formula.

Sides: a-shortest

b-mid

c-hypotenuse

angles: α-smallest

β-mid

γ-lgst

Answer 2

Draw and label a diagram!

a.

sin 25° = 40000 / d

b.

tan 25° = 40000 / d