Math, asked by prafulkamble1648, 1 year ago

the angle of elevation of the top of a tower from two points p and q at a distance of 4m and 9m respectively from the base of the tower and in the same straight line with it are 60 degrees and 30 degrees.prove that the height of the tower is 6m.

Answers

Answered by MANJAP
52
This is the answer.. given below is the answer..i hope it will help
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Answered by adith244pbxpqz
14

Answer:

Given AB is the tower.

P and Q are the points at distance of 4m and 9m respectively.

From fig, PB = 4m, QB = 9m.


Let angle of elevation from P be α and angle of elevation from Q be β.

Given that α and β are supplementary. Thus, α + β = 90

In triangle ABP,

tan α = AB/BP – (i)


In triangle ABQ,

tan β = AB/BQ

tan (90 – α) = AB/BQ (Since, α + β = 90)

cot α = AB/BQ

1/tan α = AB/BQ

So, tan α = BQ/AB – (ii)


From (i) and (ii)

AB/BP = BQ/AB

AB^2 = BQ x BP

AB^2 = 4 x 9

AB^2 = 36


Therefore, AB = 6.

Hence, height of tower is 6m.

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