NCERT Solutions · Class 10 Mathematics Some Applications of Trigonometry

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $\displaystyle 60$°. From another point $\displaystyle 20$ m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is $\displaystyle 30$° (see Fig. $\displaystyle 9.12$). Find the height of the tower and the width of the canal.

From the top of a $\displaystyle 7$ m high building, the angle of elevation of the top of a cable tower is $\displaystyle 60$° and the angle of depression of its foot is $\displaystyle 45$°. Determine the height of the tower.

As observed from the top of a $\displaystyle 75$ m high lighthouse from the sea-level, the angles of depression of two ships are $\displaystyle 30$° and $\displaystyle 45$°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

A $\displaystyle 1.2$ m tall girl spots a balloon moving with the wind in a horizontal line at a height of $\displaystyle 88.2$ m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $\displaystyle 60$°. After some time, the angle of elevation reduces to $\displaystyle 30$° (see Fig. $\displaystyle 9.13$). Find the distance travelled by the balloon during the interval.

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 $\displaystyle 30$°, 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 $\displaystyle 60$°. Find the time taken by the car to reach the foot of the tower from this point.