Some Applications of Trigonometry

This chapter has

Some Applications of Trigonometry — solved practice questions

8 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   The angle of elevation is measured from:

   • Avertical to the object
   • Bhorizontal upward to the object
   • Cobject down to horizontal
   • Dtop of object
   Show answer & solution

   Correct answer: (B) horizontal upward to the object

   Angle of elevation is the angle measured upward from the horizontal line of sight.

2. Q2easy

   The angle of depression is measured from:

   • Ahorizontal downward to the object
   • Bobject to ground
   • Cvertical to the object
   • Dground to observer
   Show answer & solution

   Correct answer: (A) horizontal downward to the object

   Angle of depression is measured downward from the horizontal to the object below.

3. Q3medium

   A person 1.8 m tall looks at the top of a tower at an angle of elevation of 45°. If the tower is 21.8 m tall, the horizontal distance from the person to the tower is:

   • A21.8 m
   • B20 m
   • C18 m
   • D22 m
   Show answer & solution

   Correct answer: (B) 20 m

   Height above eye level = 21.8 − 1.8 = 20 m. tan 45° = 1 → distance = 20 m.

4. Q4medium

   A ladder 10 m long makes an angle of 60° with the ground. The height of the wall it reaches is:

   • A5 m
   • B10 m
   • C5√3 m
   • D10√3 m
   Show answer & solution

   Correct answer: (C) 5√3 m

   Height = 10 × sin 60° = 10 × √3/2 = 5√3 m.

5. Q5hard

   From the top of a 15 m high building, the angle of depression to a car is 30°. The horizontal distance of the car from the building is:

   • A15 m
   • B15√3 m
   • C15/√3 m
   • D30 m
   Show answer & solution

   Correct answer: (B) 15√3 m

   tan 30° = 15/d → d = 15/tan 30° = 15√3 m.

6. Q6medium

   The angle of elevation of the sun, when a tree of height 6 m casts a shadow of 6 m, is:

   • A30°
   • B60°
   • C45°
   • D90°
   Show answer & solution

   Correct answer: (C) 45°

   tan θ = 6/6 = 1 → θ = 45°.

7. Q7medium

   A kite is flying at a height of 50 m. The string makes an angle of 30° with the horizontal. The length of the string is:

   • A50 m
   • B75 m
   • C100 m
   • D25 m
   Show answer & solution

   Correct answer: (C) 100 m

   sin 30° = 50/l → l = 50/(1/2) = 100 m.

8. Q8medium

   From the top of a cliff 60 m high, the angle of depression of a boat is 45°. The horizontal distance of the boat from the foot of the cliff is:

   • A30 m
   • B60 m
   • C60√3 m
   • D120 m
   Show answer & solution

   Correct answer: (B) 60 m

   tan 45° = 1 → d = 60 m.

Want the full set? Practise all 15 Some Applications of Trigonometry questions →