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The angles of elevation of the top of a tower observed from tw

Question

The angles of elevation of the top of a tower observed from two points on the ground are $3 0^{o}$ and $4 5^{o}$ . If the distance between the two points is $20$ metres, then the height of the tower is

27.3m$

17.3m

54.6$$m

None

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The angles of elevation of the top of a tower observed from two points on the ground are

3 0^{o}

and

4 5^{o}

. If the distance between the two points is

20

metres, then the height of the tower is

10 mins ago

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Text solutionVerified

Let the height of the tower be

y

△ A PB

tan 3 0^{0} \frac{y}{x + 20}

....{i}

△ A QB

tan 4 5^{0} = \frac{y}{x}

=> x = y

...................................{ii}

Putting the value of

x

in {i} we get,

\frac{1}{3} = \frac{y}{y + 20}

=> y + 20 = 3 y

=> y = \frac{20}{3 - 1}

=> y = \frac{20}{0.732}

[since

3 = 1.732

]

=> y = 27.3

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Question Text	The angles of elevation of the top of a tower observed from two points on the ground are $3 0^{o}$ and $4 5^{o}$ . If the distance between the two points is $20$ metres, then the height of the tower is
Answer Type	Text solution:1
Upvotes	150