NCERT Class 10 Chapter 9 Some Applications of Trigonometry Official CBSE Board Sample Problems Long Answer

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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

The angles of elevation

The Angles of Elevation

The angles of elevation

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

The angles of elevation

The Angles of Elevation

The angles of elevation

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,

Height of the poles.

Height of the Poles.

Height of the 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

Two poles of equal heights

Two Poles of Equal Heights

Two poles of equal heights

AB ¡s 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 ¡s 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.

The suns altitude

The Suns Altitude

The suns altitude

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

Standing on the deck of a ship

Standing on the Deck of a Ship

Standing on the deck of a ship

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

The angle of elevation

The Angle of Elevation

The angle of elevation

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

The angle of elevation

The Angle of Elevation

The angle of elevation

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 ¡s flying is 2598 m.

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