NCERT Solutions · Class 10 Mathematics Some Applications of Trigonometry

A circus artist is climbing a $\displaystyle 20$ m 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 $\displaystyle 30$° (see Fig. $\displaystyle 9.11$).

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $\displaystyle 30$° with it. The distance between the foot of the tree to the point where the top touches the ground is $\displaystyle 8$ m . 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 $\displaystyle 5$ years, she prefers to have a slide whose top is at a height of $\displaystyle 1.5$ m, and is inclined at an angle of $\displaystyle 30$° 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 $\displaystyle 60$° 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 $\displaystyle 30$ m away from the foot of the tower, is $\displaystyle 30$°. Find the height of the tower.

A kite is flying at a height of $\displaystyle 60$ m 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 $\displaystyle 60$°. Find the length of the string, assuming that there is no slack in the string.

A $\displaystyle 1.5$ m tall boy is standing at some distance from a $\displaystyle 30$ m tall building. The angle of elevation from his eyes to the top of the building increases from $\displaystyle 30$° to $\displaystyle 60$° 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 $\displaystyle 20$ m high building are $\displaystyle 45$° and $\displaystyle 60$° respectively. Find the height of the tower.

A statue, $\displaystyle 1.6$ 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 $\displaystyle 60$° and from the same point the angle of elevation of the top of the pedestal is $\displaystyle 45$°. Find the height of the pedestal.

The angle of elevation of the top of a building from the foot of the tower is $\displaystyle 30$° and the angle of elevation of the top of the tower from the foot of the building is $\displaystyle 60$°. If the tower is $\displaystyle 50$ 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 $\displaystyle 80$ m wide. From a point between them on the road, the angles of elevation of the top of the poles are $\displaystyle 60$° and $\displaystyle 30$°, respectively. Find the height of the poles and the distances of the point from the poles.