Question

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p and q are two point observed from the top of a building 10√3 m hight. If the angle of depression of the point are complementary and pq = 20m , then the distance of p from the building is?





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Answer 1

Answer:

and q are two point observed from the top of a building 10√3 m hight. If the angle of depression of the point are complementary and pq = 20m , then the distance of p from the building is?

Answer 2

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Angles of depression are x and 90-x.

Tan x = 10√3 / PR => PR = 10√3 /Tan x

Tan (90-x) = Cot x = 10√3 /QR => QR = 10√3 tanx

PR - QR = 20 m = 10√3 (1/tanx - tan x)

=> Tan² x + (2/√3) tan x - 1 = 0

=> Tan x = 1/√3 by using the solution of quadratic equation.

=> x = 30° and hence, 90 - x = 60°

Now QR = 10√3 Tan x = 10 m

=> PR = 20 +10 = 30 meters