Question

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 at a distance d = 560 m away measures the angle of elevation to the spot of light to be 45°. find the height h of the cloud cover,

Answer 1

Answer:

The height of the cloud cover is 441.66 meters

Step-by-step explanation:

Distance = 560 m

The height of the cloud cover = h meters

According to the diagram, the worker stands at point R,

Let RT = x

tan 45⁰ = $\frac{opposite}{adjacent}$ = $\frac{h}{x}$

therefore, 1 =  $\frac{h}{x}$, h = x

Then tan 75⁰ = $\frac{h}{560-x}$, substituting x = h, we have

3.732 = $\frac{h}{560-h}$

3.732(560 - h) =  h

3.732 × 560 = 3.732h + h

2089.92 = 4.732h

h = 441.66 m