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The angles of elevation of the top of a tower from two points

Question

The angles of elevation of the top of a tower from two points situated at distances $36 m$ and $64 m$ from its base and in the same straight line with it are complementary. What is the height of the tower?

50 m

48 m

25 m

24 m

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The angles of elevation of the top of a tower from two points situated at distances

36 m

and

64 m

from its base and in the same straight line with it are complementary. What is the height of the tower?

7 mins ago

Discuss this question LIVE

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Text solutionVerified

Given

A B

is the tower.

P

and

Q

are the points at distance of

36 m

and

64 m

respectively.

PB = 36 m, QB = 64 m .

Let angle of elevation from

P

α

and angle of elevation from

Q

β

Given that

α

and

β

are supplementary. Thus,

α + β = 90

In triangle

A BP

tan α = \frac{A B}{BP}

– (i)

In triangle

A BQ

tan β = \frac{A B}{BQ}

tan (90- α) = \frac{A B}{BQ}

cot α = \frac{A B}{BQ}

\frac{1}{tan α} = \frac{A B}{BQ}

So,

tan α = \frac{BQ}{A B}

– (ii)

From (i) and (ii)

\frac{A B}{BP} = \frac{BQ}{A B}

A B^{2} = BQ \times BP

A B^{2} = 36 \times 64

A B^{2} = 2304

Therefore,

A B = 48

Hence, height of tower is

48 m

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Question Text	The angles of elevation of the top of a tower from two points situated at distances $36 m$ and $64 m$ from its base and in the same straight line with it are complementary. What is the height of the tower?
Answer Type	Text solution:1
Upvotes	150

The angles of elevation of the top of a tower from two points situated at distances 36 m and 64 m from its base and in the same straight line with it are complementary. What is the height of the tower?

Text solutionVerified

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The angles of elevation of the top of a tower from two points situated at distances $36 m$ and $64 m$ from its base and in the same straight line with it are complementary. What is the height of the tower?