ind below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Introduction to Trigonometry and its Applications:

Exercise 8.3

Short Answer Type Questions (Q. No. 8-15)

Question. 10 A ladder 15m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then find the height of the wall.

Solution.

Let AB be the 15 m long ladder making a 60^o angle with a h metre high wall AC.

Question. 11 Simplify (1 + tan² θ) (1 - sin θ) (1 + sin θ).

Solution.

Question. 12 If 2sin²θ - cos²θ = 2, then find the value of θ.

Solution.

Question. 14 An observer 1.5m tall is 20.5m away from a tower 22m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Solution.

Let AB be the 22 m high tower and CD be the 1.5 m tall observer standing at a distance of BC = 20.5 m away from the tower.

Also, let θ be the angle of elevation of the top of the tower from the eye of the observer.

Question. 15 Show that tan⁴θ + tan² θ = sec⁴ θ - sec² θ.

Solution.