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From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill?

From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill? Correct Answer 48

In △ABE

tan30 = AB/BE

1/√3 = 12/BE

BE = 12√3

As we know,

BE = AD and AB = DE

In △ACD

tan60 = CD/AD

√3 = CD/12√3

CD = 12√3 × √3 = 36

CE = CD + DE

CE = 36 + 12 = 48 m

SHORT TRICK:

1 unit = 12

4 unit = 12 × 4 = 48 cm

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