Class 10 - Chapter 9: Applications of Trigonometry

Section A (1 Mark each)

Q1. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is $30^\circ$. The height of the tower is:

(a) $10\sqrt{3}$ m (b) $30\sqrt{3}$ m (c) $10$ m (d) $30$ m

Q2. A pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground. The sun's elevation is:

(a) $60^\circ$ (b) $45^\circ$ (c) $30^\circ$ (d) $90^\circ$

Q3. If the length of the shadow of a tower is increasing, then the angle of elevation of the sun:

(a) is also increasing (b) is decreasing (c) remains unchanged (d) none of these

Q4. Assertion (A): If the length of shadow of a vertical pole is equal to its height, then the angle of elevation of the sun is $45^\circ$.
Reason (R): According to Pythagoras theorem, $h^2 + l^2 = (\text{hypotenuse})^2$.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. A circus artist is climbing a 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 $30^\circ$.

Solve on white paper.

Q6. A kite is flying at a height of 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 $60^\circ$. Find the length of the string, assuming that there is no slack in the string.

Solve on white paper.

Q7. An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45^\circ$. What is the height of the chimney?

Solve on white paper.

Section C (3 Marks each)

Q8. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are $30^\circ$ and $45^\circ$ respectively. If the lighthouse is 100 m high, find the distance between the two ships.

Solve on white paper.

Q9. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^\circ$ with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Solve on white paper.

Section D (5 Marks)

Q10. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is $60^\circ$ and the angle of depression of its foot is $45^\circ$. Determine the height of the tower.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study:

A group of students of class X visited India Gate on an education trip. The teacher narrated that India Gate is about 42 metres in height.

(i) What is the angle of elevation if they are standing at a distance of 42 m from the monument?

(ii) They want to see the top of the monument at an angle of $60^\circ$. Find the distance where they should stand.

(iii) If the altitude of the Sun is at $60^\circ$, then what is the height of a vertical tower that will cast a shadow of length 20 m?

Solve on white paper.