HARD
10th CBSE
IMPORTANT
Earn 100

A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff. 

Important Questions on Heights & Distances

HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 32
From the terrace of a house 8 m high, the angle of elevation of the top of a tower is 45° and the angle of depression of its reflection in a lake is found to be 60°. Determine the height of the tower from the ground. 
HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 33
The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is 30°. On advancing 'p' metres towards the foot of the tower, the angle of elevation becomes 45°. Show that the height h'' of the tower is given by h=(3+1)p2.
Also, determine the height of the tower, if p=150 metres, α=30° and β=60°.
HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 34

The angle of elevation of an aeroplane as observed from a point 10 m above the ground is found to be 30° and the angle of depression of its reflection in a lake is found to be 60°. Determine the height of the aeroplane from the ground. 

HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 35
A round balloon of radius 'a' subtends an angle θ at the eye of the observer while the angle of elevation of its centre is ϕ. Prove that the height of the centre of the balloon is asinϕcosecθ/2.
 
HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 36
A surveyor noted that the angle of elevation of a marker on the top of a hill was 30°. He walked 40 m towards the foot of the hill along level ground and found the angle of elevation of the marker as 45°. If the surveyor's first position was the marker at k3+1m, then find the value of k.
HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 37
A fire at a building B is reported on telephone to two fire stations F1 and F2,10 km apart from each other on a straight road. F1 observes that the fire is at angle of 60° to the road and F2 observes that it is at angle of 30° from it. Which station should send his team and how much will it have to travel?
HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 38
A parachutist is descending vertically and makes angles of depression of 45° and 60° at two observation points 100 m apart from each other on the left side of himself. Find, in metres, the approximate height from which he falls and also find, in metres the approximate distance of the point, where he falls on the ground from the first observation point. 
HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 39
The line joining the top of a hill to the foot of the hill makes angle of 30° with the horizontal through the foot of the hill. There is one temple at the top of the hill and a guest house half way from the foot to the top. The tops of the temple and of the guest house both make an elevation of 45° at the foot of the hill. If the guest house is 100 m away from the foot of the hill along the hill, find the heights of the guest house and the temple.