Doubt Solutions for chapter 11. Some Applications of Trigonometry class 10 - Maths, CBSE, NCERT

A circus artist is climbing a $20m$ long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30%5E%7Bo%7D$ (see figure).

Exercise11.1(A), Question No.1

A circus artist is climbing a $20m$ long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30%5E%7Bo%7D$ (see figure).

A tree breaks due to storm and the broken part bends so
that the top of the tree touches the ground making an angle $30%5E%7Bo%7D$ with it.
The distance between the foot of the tree to the point where the top
, touches the ground is $8m.$ Find the height of the tree.

Exercise11.1(A), Question No.2

A tree breaks due to storm and the broken part bends so
that the top of the tree touches the ground making an angle $30%5E%7Bo%7D$ with it.
The distance between the foot of the tree to the point where the top
, touches the ground is $8m.$ Find the height of the tree.

A contractor plans to install two slides for the children to play in a park, for the children below the age of $5+$ years, she prefers to have a slide whose top is at a height of $1.5m$ ,and is inclined at an angle of $30%5E%7Bo%7D$ to the ground, whereas for elder children, she wants to have a steep slide at a height of $3m$ and inclined at an angle of $60%5E%7Bo%7D$ to the ground. What should be the length of the slide in each case?

Exercise11.1(A), Question No.3

A contractor plans to install two slides for the children to play in a park, for the children below the age of $5+$ years, she prefers to have a slide whose top is at a height of $1.5m$ ,and is inclined at an angle of $30%5E%7Bo%7D$ to the ground, whereas for elder children, she wants to have a steep slide at a height of $3m$ and inclined at an angle of $60%5E%7Bo%7D$ to the ground. What should be the length of the slide in each case?

The angle of elevation of the top of a tower from a point
on the ground, which is $30+%5C%3Bm$ away from the foot of the tower, is $30%5E%7B%5Ccirc%7D$
Find the height of the tower.

Exercise11.1(A), Question No.4

The angle of elevation of the top of a tower from a point
on the ground, which is $30+%5C%3Bm$ away from the foot of the tower, is $30%5E%7B%5Ccirc%7D$
Find the height of the tower.

A kite is flying at a height of 60m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60%5E%7Bo%7D$ . Find the length of the string, assuming that there is no slack in the string.

Exercise11.1(A), Question No.5

A kite is flying at a height of 60m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60%5E%7Bo%7D$ . Find the length of the string, assuming that there is no slack in the string.

A $1.5%5C%3Bm$ tall boy is standing at some distance from a $30%5C%3Bm$ tail building $.$ The angle of elevation from his eyes to the top of the building increases from $30%5E%7Bo%7D$ to $60%5E%7Bo%7D$ as he walks towards the building $.$ Find the distance he walked towards the building $.$

Exercise11.1(A), Question No.6

A $1.5%5C%3Bm$ tall boy is standing at some distance from a $30%5C%3Bm$ tail building $.$ The angle of elevation from his eyes to the top of the building increases from $30%5E%7Bo%7D$ to $60%5E%7Bo%7D$ as he walks towards the building $.$ Find the distance he walked towards the building $.$

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45%5E%7Bo%7D$ and $60%5E%7Bo%7D$ respectively. Find the height of the tower.

Exercise11.1(A), Question No.7

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45%5E%7Bo%7D$ and $60%5E%7Bo%7D$ respectively. Find the height of the tower.

A statue, $1.6%5C+m$ tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60%5E%7Bo%7D$ and from the same point the angle of elevation of the top of the pedestal is $45%5E%7Bo%7D$ . Find the height of the pedestal.

Exercise11.1(A), Question No.8

A statue, $1.6%5C+m$ tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60%5E%7Bo%7D$ and from the same point the angle of elevation of the top of the pedestal is $45%5E%7Bo%7D$ . Find the height of the pedestal.

The angle of elevation of the top of a building from the
foot of the tower is $30%5E%7B%5Ccirc+%7D$ and the angle of elevation of the top·of the tower from the foot of the building, is $60%5E%7Bo%7D$ If the tower is
50 m high, .find the height of the
building.

Exercise11.1(A), Question No.9

The angle of elevation of the top of a building from the
foot of the tower is $30%5E%7B%5Ccirc+%7D$ and the angle of elevation of the top·of the tower from the foot of the building, is $60%5E%7Bo%7D$ If the tower is
50 m high, .find the height of the
building.

Two poles of equal heights are standing opposite each other on either side of the road, which is $80+m+$ wide. From a point between them on the road, the angles of elevation of the top of the poles respectively are $60%5E%7Bo%7D$ and $30%5E%7Bo%7D$ . Find the height of the poles and the distances of the point from the poles.

Exercise11.1(A), Question No.10

Two poles of equal heights are standing opposite each other on either side of the road, which is $80+m+$ wide. From a point between them on the road, the angles of elevation of the top of the poles respectively are $60%5E%7Bo%7D$ and $30%5E%7Bo%7D$ . Find the height of the poles and the distances of the point from the poles.