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,
1 answer:
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 =
= 
therefore, 1 =
, h = x
Then tan 75⁰ =
, substituting x = h, we have
3.732 = 
3.732(560 - h) = h
3.732 × 560 = 3.732h + h
2089.92 = 4.732h
h = 441.66 m
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