EXTRA QUESTIONS (Application of trigonometry) SET-1

PODAR INTERNATIONAL SCHOOL (CBSE)  

Topic :Heights & Distances  

1. From a point A, in level with the foot of a vertical pole 25m from it, the angle of
elevation of the top of the pole from point A is 30°.Calculate the height of the pole.

2.    A tree casts a shadow 4m long on the ground when the angle of elevation of the Sun
is 45°.Find the height of the tree.  

3.  An electrician has to repair an electric fault on apole of height 4m. He needs to
reach a point 1.3 m below the top of the pole to undertake the repair work. What
should be the length of the ladder that he should use which when inclined at an
angle of 60 to the horizontal would enable him to reach the required position?

4.    While dashing to the destination point on the ground, the pilot of the aeroplane
declines his aeroplane by 30°and drives straight to the ground. The average speed
of the aeroplane is 200 km/hr. It takes 54 seconds to reach the ground. How high
was the aeroplane before it started its dash ?

5. The shadow of a flag staff is three times as long as its shadow, when the sunrays
meet the ground at an angle of 60°. Find the angle between the sunrays and the
ground at the time of the longer shadow.

6.    A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from
him at an elevation of 30°.A girl standing on the roof of a 20 m high building ,
finds the angle of elevation of the same bird to be45°.Both the boy and girl are
on the opposite sides of the bird. Find the distance of the bird from the girl.

7.    A man on the top of a vertical observation tower observes a car moving at a uniform
speed coming directly towards it. If it takes 12 minutes for the angle of depression to
change from 30°to 45°, how soon after this will the car reach the tower ? Give your
answer correct to the nearest second.

8.    The angle of elevation of the top Q of a vertical tower PQ from a point X on the
ground is 60°.At a point Y, 40 m vertically above X, the angle of elevation is 45°.
Find the height of the tower PQ and the distance XQ.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>