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A flag is placed on the top of a temple. The angles of elevation of the top of the flag and the top of the temple from point 15 m away from the base of the temple are 60° and 45°, respectively. What is the length of the pole of the flag? 

A flag is placed on the top of a temple. The angles of elevation of the top of the flag and the top of the temple from point 15 m away from the base of the temple are 60° and 45°, respectively. What is the length of the pole of the flag?  Correct Answer 15(√3 - 1) m 

Given:

A flag is placed on the top of a temple. The angles of elevation of the top of the flag and the top of the temple from point 15 m away from the base of the temple are 60° and 45°, respectively.

Formula Used:

tan 45° = 1 = P/B; tan 60° = √3

Calculation:

Let the length of the pole of the flag be 'x' m

From ∆ BDC, we have 

⇒ tan 45° = BC/CD = BC/15

⇒ BC = 15 m

From ∆ ADC, we have

⇒ tan 60° = AC/CD = AC/15

⇒ AC = 15√3

length of the pole of the flag = (AC - BC) = (15√3 - 15) m = 15(√3 - 1) m 

∴ required length of the pole of the flag = 15(√3 - 1) m.            

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