MEDIUM
10th CBSE
IMPORTANT
Earn 100

Two stations due south of a leaning tower which leans towards north are at distances a and b from its foot. If α and β be the elevations of the top of the tower from these stations, prove that its inclination θ to the horizontal is given by cotθ=bcotα-acotβb-a

Important Questions on Heights & Distances

HARD
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 42
A man on the top of a vertical 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?
MEDIUM
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 43
The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sunrays meet the ground at an angle of 60°. Find the angle between the sunrays and the ground at the time of longer shadow. 
MEDIUM
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 44
The angle of elevation of a stationary cloud from a point 2500 m above a lake is 30° and the angle of depression of its reflection in the lake is 45°. What is the height of the cloud above the lake level?
MEDIUM
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 45
If the angle of elevation of a cloud from a point h meters above a lake is α and the angle of depression of its reflection in the lake is β, prove that the height of the cloud is h(tanβ+tanα)tanβ-tanα.
 
MEDIUM
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 46
The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree, when seen from the top of the second tree is 45°. If the height of the second tree is 80 m, find the height of the first tree.
MEDIUM
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 47
From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the lighthouse be h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is h(tanα+tanβ)tanαtanβ meters.
MEDIUM
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 48
A tower subtends an angle α at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b meters just above A is β. Prove that the height of tower is btanαcotβ.
MEDIUM
10th CBSE
IMPORTANT
New Mathematics for Class X>Chapter 9 - Heights & Distances>EXERCISE>Q 49

PQ is a post of given height a and AB is a tower at some distance, α and β are the angles of elevation of B, the top of the tower, at P and Q respectively. Find the height of the tower and its distance from the post.