What is the height of the building?

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Solution

Q.
Rohit is standing at the top of a building and observes a car at an angle of depression of $30 °$ as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to $60 °$ , and at that moment, the car is 25 m away from the building.

Based on the above information, answer the following questions:

(i) What is the height of the building

1 $25 \sqrt{3} m$

2 $25 \sqrt{- 3} m$

3 $25 \sqrt{2} m$

4 $24 \sqrt{3} m$

Ans.
(1)

From the figure:

$∠ D A M = ∠ A D B = 30 ° and ∠ C A M = ∠ A C B = 60 ° (A l t e r n a t e a n g l e s) I n ∆ A B C t a n 60 ° = \frac{A B}{B C} \sqrt{3} = \frac{A B}{25} \Rightarrow A B = 25 \sqrt{3} H e n c e, Height of building = 25 \sqrt{3} m$

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