Application of Trigonometry

A tree casts a shadow of length 15 m when the angle of elevation of the sun is 30°. What is the height of the tree? (Use \( \tan 30° = \frac{1}{\sqrt{3}} \))

From the top of a building 50 m high, the angle of depression of the base of a tower is 45° and the angle of elevation of its top is 30°. Find the height of the tower.

A ladder 10 m long rests against a wall making an angle of 60° with the ground. How high does the ladder reach on the wall?

An observer standing at a point sees the top of a tower at an angle of elevation 45°. If the observer moves 20 m closer, the angle of elevation becomes 60°. Find the height of the tower.

If \( \sin \theta = \frac{3}{5} \), find \( \cos \theta \) and \( \tan \theta \).

A man standing on the ground observes the top of a pole at an angle of elevation 30°. If he moves 10 m closer, the angle of elevation becomes 60°. Find the height of the pole.

The angle of elevation of the top of a tower from a point on the ground is 45°. After walking 50 m towards the tower, the angle of elevation becomes 60°. Find the height of the tower.

A kite is flying at a height of 60 m. The angle of elevation of the kite from two points on the ground which are 80 m apart in a line towards the kite are 30° and 60°. Find the distance of the kite from the two points.

In a right triangle, if one acute angle is 45° and the hypotenuse is 10 cm, find the length of the side opposite to 45°.

A man standing on the ground observes the top of a tower at an angle of elevation of 60°. He then moves 10 m towards the tower and the angle of elevation becomes 90°. Find the height of the tower.