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The angle of elevation of a tower CD at a place A due to south

Question

The angle of elevation of a tower $C D$ at a place $A$ due to south of it is $60$ and at a place $B$ due west of $A$ , the elevation is $30$ . if $A B = 3 km$ , then find the height of tower.

0.95 km

200 m

173.2 m

141.4 m

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Mila Discussed

The angle of elevation of a tower

C D

at a place

A

due to south of it is

60

and at a place

B

due west of

A

, the elevation is

30

. if

A B = 3 km

, then find the height of tower.

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

We have,

C D a s t h e g i v e n t o w er .

L e t ∠ D A C = 6 0^{0}

L e t h = h e i g h t o f t o w er = C D

I n Δ A D C, cot 6 0^{0} = \frac{D A}{C D} \Rightarrow \frac{1}{3} = \frac{D A}{h} \Rightarrow D A = \frac{h}{3} ....... (1) I n Δ B D C, cot 3 0^{0} = \frac{B D}{C D} \Rightarrow 3 = \frac{B D}{h} ......... (2)

I n Δ A D B, A B^{2} = A D^{2} + B D^{2} (3)^{2} = (\frac{h}{3})^{2} + (3 h)^{2} \Rightarrow 9 = (\frac{h ^{2}}{3}) + (3 h)^{2} \Rightarrow 10 h^{2} = 9 \Rightarrow h^{2} = \frac{9}{10} \Rightarrow h = \frac{3}{10} = \frac{3 10}{10} = \frac{3 \times 3.162}{10} = 0.9486 km = 0.95 km

Hence, this is the answer.

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Question Text	The angle of elevation of a tower $C D$ at a place $A$ due to south of it is $60$ and at a place $B$ due west of $A$ , the elevation is $30$ . if $A B = 3 km$ , then find the height of tower.
Answer Type	Text solution:1
Upvotes	151