Question

A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 30,000 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 27°. (Round your answers to the nearest foot.)

(a) What is the distance between the plane and the arch?
(b) What is the distance between a point on the ground directly below the plane and the arch?

Answer 1

X = 33,669.78 ft

Y = 15285.76 ft

Explanation:

Given data:

let x be the distance btwn arch and plane

and y be the distance btwn ground point and arch y

we know that

`cos\theta =  (adjacent)/(hypotaneous)`

`cos(27) = (30,000)/(x)`

xcos27 = 30000

`x = (30000)/(cos 27)`

x = 33,669.78 ft

b) we knwo that

`tan \theta  = (opposite)/(adjacent)`

`tan 27 = (y)/(30000)`

y = tan(27) (30000)

y = 15285.76 ft