# NCERT Class 10 Chapter 9 Some Applications of Trigonometry Official CBSE Board Sample Problems Long Answer (For CBSE, ICSE, IAS, NET, NRA 2023)

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## Question

**The angles of elevation of the top of a tower from two points at a distance of 4 m and 9m from the base of the tower and in the same straight line with it are** **and** **respectively. Find the height of the tower**.

### Solution

Let AB be the tower of height ‘h’ .

In

## Question

**A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is** . **The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is** . **Find the speed of flying of the bird**.

### Solution

Let BC is 80 m high tree.

After 2 seconds, position of bird is E.

Let

In

In

x 80 (1.732 — I) x — 80x0.732

So, the speed of flying of the bird

## Question

**Two poles of equal heights are standing opposite to each other on either side of the road, which is 100 m wide. From a point between them on the road. The angles of elevation of the top of the poles are 60 and 30 respectively. Find the height of the poles**.

### Solution

In

In

Height of poles,

## Question

**Two poles of equal heights are standing opposite to each other on either side of the road, which is loo m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60 and 30 respectively. Find the height of the poles**.

### Solution

AB is a building of height 7m and CD is a tower of height h

In ⧵ big triangle up AED

In ⧵big triangle up AEC

Height of the tower is 28m

## Question

**A vertical pedestal stands on the ground and is surmounted by a vertical flagstaff of height 5 m. At a point on the ground, the Angles of elevation of the bottom and the top of the flagstaff are 30 and 60⧵text degree respectively. Find the height of the pedestal**.

### Solution

Let height of the pedestal AB = h and BC is the vertical staff of height = 5 cm

In ⧵ big triangle up BAO

In⧵big triangle up CAO

Height of the padestal is 2.5 m

## Question

**The shadow of a tower standing on a level ground is found to be 20 m longer when the suns altitude is 45 than when it is 60. Find the height of the tower**.

## Question

**The angle of elevation of an aeroplane from a point on the ground is** . **After flying for 15 seconds, the elevation changes to** . **If the aeroplane is flying at a height of 2500 m, find the speed of the aeroplane**.

## Question

**A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of**, **which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be**. **Find the time taken by the car to reach the foot of the tower from this point**.

## Question

**The angle of elevation of a jet plane from a point A on the ground is** . **After a flight of 30 seconds, the angle of elevation changes to**. **If the jet plane is flying at a speed of 864kmph, find the height at which the jet plane is flying. (use****)**

## Question

**The angle of elevation of a stationary cloud from a point 200 m above the lake is 30 degrees and the angle of depression of its reflection in the lake is found to be 60 degrees. Find the height of the cloud**.

### Solution

A is the position of the cloud, B is the point 200m above the lake and F is the reflection of A in the lake.

Now,

Now, from triangle ABC we have,

In triangle CFB we have,

So,

From (j) and (ii) we get,

Hence, height of the cloud AE 200 + m 200 + 200 400 metres

## Question

**A man standing on the deck of a ship, which is 10m above water level. He observes the angle of elevation of the top of a hill as** **and the angle of depression of the base of the hill as** . **Calculate the distance of the hill from ship and the height of the hill**.

### Solution

Let a man is standing on the deck of a ship at point A such that AB = 10 m & let CD be the hill. Thus,

Let &

In

In

The height of the hill is

Hence, the height of the hill is 40 m & the Distance of the hill from the ship is 1 013 m.

## Question

**A kite is flying at a height of 30 m from the ground. The length of the string from kite to the ground is 60 m. Assuming that there is no slack in the string; find the angle of elevation of the kite at the ground**.

### Solution

Let point A be the position of the kite and AC be its string

We have,

and

Let

In ,

## Question

**The angle of elevation of a jet fighter from a point A on the ground is** . **After a flight of 15 seconds the angle of elevation changes to**. **If the jet is flying at the speed of 720 km/h, find the constant height at which jet is flying. (Use****)**

### Solution

Let A be the point of observation on the ground and B and C be the two positions of the jet. Let metres.

Let metres.

Speed of the jet me taken to cover the distance BC is 1 5 sec.

Distance

In ,

In ,

From (j) and (ii)

Thus, the height at which the jet is flying is 2598 m.