NCERT Class 10 Chapter 9 Some Applications of Trigonometry Official CBSE Board Sample Problems Short Answer (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question

An aeroplane, when flying at a height of 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are and respectively. Find the vertical distance between the aeroplanes at that instant.

Solution

Let y is the vertical distance between the aeroplanes.

In

… (i)

Now, in

[From (i) ]

So, distance between the aeroplanes is 2920 m.

Question

A 7 m long flagstaff is fixed on the top of a tower standing on the horizontal plane. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are and respectively. Find the height of the tower correct to one place of decimal

Solution

Let AB is the tower of height h and DA is the flagstaff of height 7 m and BC is x.

In

Now, in ,

So, height of the tower is 9.5 m.

Question

Two men on either side of a 75 m high building and in line with base of building observe the angles of elevation of the top of the building as and . Find the distance between the two men

Solution

Let C and D be the positions of two men. A

Let and

In

Now, in MBD,

Hence, distance between two men is

Question

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

Solution

Let AB be the water level, DA be the height of ship = 10 m.

Let BC be the hill of height h from water level.

In

. . (i)

Now, in

= (From (i) ]

So, distance of hill from ship and the height of the hill = 40m.

Question

The angles of depression of the top and bottom of a 50m high building from the top of a tower are and respectively. Find the height of the tower and the horizontal distance between the tower and the building,

Solution

Let CD is the building of height 50 m and AB be the tower.

Let horizontal distance between the tower and building is BC is x metre.

: BCDE is a rectangle A

So, and

Also, and

Let

Now, in

. . (i)

Now, in

Height of the tower

118.25m

Horizontal distance between the tower and the building

Question

A 7 m long flagstaff is fixed at the top of a tower standing on the horizontal plane. From a point on the ground, the angle of elevation of the top and bottom of the flagstaff are 60 and 45 respectively. Find the height of the tower correct to one place of decimal. (Use )

Solution

Let AB is the height of the tower be h and AD is the height of the flagpole is 7 m and BC

In

Question

Two men on either side of a 75 m high building and in line with the base of building observe the angles of elevation of the top of the building as 30 and 60. Find the distance between the two men

Solution

Let C and D be the positions of two men, and

In,

Distance between two men is

Question

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 m away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60 and 30 respectively. Find the heights of the tower and the flag pole mounted on it.

) .

Solution

In

Height of the tower

Height of the flagpole

Question

A man standing on the deck of a ship, which is 10 m above the water level. Observes the angle of elevation is the top of a hill as 60 and the angle of depression of the base of the hill as 30. Find the distance of the hill from the ship and the height of the hill.

Solution

Distance of the cliff

Height of the cliff

A

E

Question

Due to a storm the upper part of a tall tree broke and got bent. Its top struck the ground at a distance of 8 m from its base making an angle of 30 degrees with the ground. What was the height of the tree?

Solution

Let AB be the part of the tree still attached and AC the part fallen to the ground

So the height of the tree was