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Fittoniya [83]
3 years ago
7

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?

Mathematics
1 answer:
Maurinko [17]3 years ago
8 0

Answer:

X = 33,669.78 ft

Y = 15285.76 ft

Step-by-step 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 =  \frac{adjacent}{hypotaneous}

cos(27) = \frac{30,000}{x}

xcos27 = 30000

x = \frac{30000}{cos 27}

x = 33,669.78 ft

b) we knwo that

tan \theta  = \frac{opposite}{adjacent}

tan 27 = \frac{y}{30000}

y = tan(27) (30000)

y = 15285.76 ft

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