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From a point on the ground the angles of elevation of the bott

Question

From a point on the ground the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20 m high building are $4 5^{\circ}$ and $6 0^{\circ}$ respectively. Find the height of the tower ?

203 m

60 m

20 (3 - 1) m

403 m

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From a point on the ground the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20 m high building are

4 5^{\circ}

and

6 0^{\circ}

respectively. Find the height of the tower ?

14 mins ago

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14 mins ago

Text solutionVerified

Let PQ be the building of height

20

metres,
AP be the transmission tower of height

x

metres.
Let B be the point from where angles of elevation are drawn

∠ PBQ = 4 5^{\circ}, ∠ A BQ = 6 0^{\circ}

I n Δ PBQ, \frac{PQ}{BQ} = tan 4 5^{\circ} \Rightarrow BQ = PQ = 20 m

I n Δ A BQ, \frac{A Q}{BQ} = tan 6 0^{\circ} \Rightarrow \frac{x + 20}{20} = 3 \Rightarrow x + 20 = 203 \Rightarrow x = 203 - 20 = 20 (3 - 1)

metres

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Question Text	From a point on the ground the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20 m high building are $4 5^{\circ}$ and $6 0^{\circ}$ respectively. Find the height of the tower ?
Answer Type	Text solution:1
Upvotes	150