Trigonometry question: The angle of elevation of a cloud from a point 25 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°.What is distance between lake and the cloud?
Answers
Answer:
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Point g is the cloud.
point a is 25 m above the lake.
BC is the surface of lake
GE is the distance of cloud from the surface of lake.
GE = ED.
In triangle AGF
tan30° = FG/ AF
1/√3 = b/AF
AF = b√3
AF = CD
In triangle ACD
tan 60° = AC/ CD
√3 = 25+25+b / √3b
3b = 50+b
2b = 50
b = 50/2
b = 25 meters
So distance of cloud from surface of lake = GB
GB = 25+ b
b = 25. ( prove above)
GB = 25+25 = 50 meters.
GE = distance of cloud from the surface of lake.
ED = reflection of cloud in the lake .
That's why the distance of GE and ED is equal
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Distance between lake and cloud is 50 meters.
Hope it may help you ♥
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