MATH 127 Precalculus II Sample Test I May 20 2016 Problem 7

MATH 127 Precalculus II - Sample Test I May 20, 2016 Problem 7. To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. An observer 600 m away measures the angle of elevation to the spot of light to be 45°. Find the height h of the cloud cover (tan(75v3.) 45° 75° 600 m

Solution

Let x be the distance from observer to the cloud height (h).Then the distance from  the cloud height (h) to the spotlight is 600-x

We know the Tan75⁰ =(600-x)/h------------(1)

Tan45⁰ =x/h----------------(2)

From equation 2 we get x=h since Tan45⁰=1

From equation 1 we get h=(600-x)/Tan75⁰ =(600-x)/(2+ 3) since Tan75⁰= 2+ 3

From equation 1 and 2 x=h=(600-x)/(2+ 3)

x(2+ 3)=(600-x)

2x+3x+x=600

(3+3)x=600 then x=600/(3+3)

Therefore the height h of the cloud cover is 600/(3+3)