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Heights Distances

Q1.

The length of the shadow of a vertical tower on level ground increases by 400 feet, when the angle of elevation of the sun changes from 45° to 30°. Find the height of the tower correct to one decimal place. Take √3 = 1.73?

 

 

 

 

 

 

Q2.

From the top of a hill, the angles of depression of two consecutive mile stones to the east are found to be 30° and 45°. Find the height of the hill. Take √3 = 1.73?

 

 

 

 

 

 

Q3.

A man on the top of a vertical tower observes a car moving at a uniform speed coming towards the tower. It takes 720 seconds for the angle of depression to change from 30° to 45°. How much time from now, will it take the car to reach the tower?

 

 

 

 

 

 

Q4.

The angles of elevation of the top of a hill at the city centers of two towns on either side of the hill are observed to be 30° and 60°. The distance uphill from the first city center is 9 miles. Find the distance uphill from the other city centre?

 

 

 

 

 

 

Q5.
The angle of elevation of a cloud from a point ‘h’ feet above a lake is and the angle of
depression of its reflection in the lake is ’. What is the height of the cloud?

 

 

 

 

 

 

 

Q6.

At the foot of a mountain the elevation of its summit is 45°. After climbing 1000 feet towards the summit, at a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain?

 

 

 

 

 

 

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