Some Applications of Trigonometry: 1 mark Questions (CBSE Class 10)

A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is $10\sqrt{3}$ m away from the base of the tower, is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$90^{\circ }$
4. (D)$60^{\circ }$

The string of a flying kite is tied to a point on the ground. The length of the string between the kite and the point on the ground is 80 m. The string makes an angle of $30^{\circ }$ with the ground. The height of the kite above the ground is :

1. (A)$20\sqrt{3}$ m
2. (B)40 m
3. (C)$40\sqrt{3}$ m
4. (D)$80\sqrt{3}$ m

From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be $45^{\circ }$. The height (in metres) of the tower is :

1. (A)$10\sqrt{3}$
2. (B)$30\sqrt{3}$
3. (C)60
4. (D)30

If the length of the shadow of a tower is $\sqrt{3}$ times that of its height, then altitude of the Sun is :

1. (A)$45^{\circ }$
2. (B)$30^{\circ }$
3. (C)$60^{\circ }$
4. (D)$15^{\circ }$

A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as $60^{\circ }$. If AB = $5\sqrt{3}$ m, then length of the wire is

1. (A)10 m
2. (B)$10\sqrt{3}$ m
3. (C)15 m
4. (D)$\frac{5}{2}\sqrt{3}$ m

In the given figure, which of the following angles represents the angle of depression ?

1. (A)$x$
2. (B)$y$
3. (C)$z$
4. (D)$a$

The length of the shadow of a tower when the sun’s altitude changes from $30^{\circ }$ to $60^{\circ }$ will :

1. (A)become shorter
2. (B)become longer
3. (C)remain same
4. (D)be doubled

In the given figure, the angle of elevation of point A from point C is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)Cannot be determined

If the length of the shadow of a tower is $\sqrt{3}$ times its height, then the angle of elevation of the sun is

1. (A)$45^{\circ }$
2. (B)$30^{\circ }$
3. (C)$60^{\circ }$
4. (D)$0^{\circ }$

A kite is flying at a height of $150$ m from the ground. It is attached to a string inclined at an angle of $30^{\circ }$ to the horizontal. The length of the string is :

1. (A)$100\sqrt{3}$ m
2. (B)$300$ m
3. (C)$150\sqrt{2}$ m
4. (D)$150\sqrt{3}$ m

A ladder $14$ m long leans against a wall. If the foot of the ladder is $7$ m from the wall, then the angle of elevation of the top of the wall is :

1. (A)$15^{\circ }$
2. (B)$30^{\circ }$
3. (C)$45^{\circ }$
4. (D)$60^{\circ }$

Assertion (A) : A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the wall up to which the ladder reaches is 8 m, then the length of the ladder is 10 m.
Reason (R): The ladder makes an angle of $60^{\circ }$ with the ground.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

A 30 m long rope is tightly stretched and tied from the top of pole to the ground. If the rope makes an angle of $60^{\circ }$ with the ground, the height of the pole is :

1. (A)$10\sqrt{3}$ m
2. (B)$30\sqrt{3}$ m
3. (C)15 m
4. (D)$15\sqrt{3}$ m

An observer 1.8 m tall stands away from a chimney at a distance of 38.2 m along the ground. The angle of elevation of top of chimney from the eyes of observer is $45^{\circ }$. The height of chimney above the ground is

1. (A)38.2 m
2. (B)36.4 m
3. (C)40 m
4. (D)$(38.2)\sqrt{2}$ m

A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

If a pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground, then the sun’s elevation is

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

A pole $7\sqrt{3}$ m high casts a shadow 21 m long on the ground, then the sun’s elevation is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

A lamp post 9 m high casts a shadow $3\sqrt{3}$ m long on the ground. The Sun’s elevation at this moment is :

1. (A)$60^{\circ }$
2. (B)$90^{\circ }$
3. (C)$45^{\circ }$
4. (D)$30^{\circ }$

A tree casts a shadow 7 m long on the ground, when the angle of elevation of the Sun is $45^{\circ }$. The height of the tree is :

1. (A)$7\sqrt{3}$ m
2. (B)$\frac{7}{3}\sqrt{3}$ m
3. (C)7 m
4. (D)3.5 m

A lamp post 15 m high, casts a shadow $5\sqrt{3}$ m long on the ground. The Sun's elevation at this moment is :

1. (A)$90^{\circ }$
2. (B)$60^{\circ }$
3. (C)$45^{\circ }$
4. (D)$30^{\circ }$

From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be $60^{\circ }$. The height (in metres) of the tower is :

1. (A)$10\sqrt{3}$
2. (B)$30\sqrt{3}$
3. (C)60
4. (D)30

At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun’s altitude at that time is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

The ratio of the length of a pole and its shadow on the ground is $1:\sqrt{3}$. The angle of elevation of the Sun is :

1. (A)$90^{\circ }$
2. (B)$60^{\circ }$
3. (C)$45^{\circ }$
4. (D)$30^{\circ }$

The length of the shadow of a tower on the plane ground is $\sqrt{3}$ times the height of the tower. The angle of elevation of the Sun is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

The angle subtended by a vertical pole of height 100 m at a point on the ground $100\sqrt{3}$ m from the base is, has measure of

1. (A)$90^{\circ }$
2. (B)$60^{\circ }$
3. (C)$45^{\circ }$
4. (D)$30^{\circ }$

The angle subtended by a tower of height 200 metres at a point 200 metres from the base is

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$0^{\circ }$

The string of a kite in air is 50 m long and it makes an angle of $60^{\circ }$ with the horizontal. Assuming the string to be straight, the height of the kite from the ground is :

1. (A)$50\sqrt{3}$ m
2. (B)$\frac{100}{\sqrt{3}}$ m
3. (C)$\frac{50}{\sqrt{3}}$ m
4. (D)$25\sqrt{3}$ m

The angle of elevation of the top of a 30 m high tower at a point 30 m away from the base of the tower is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

The angle of elevation of the top of a 15 m high tower at a point $15\sqrt{3}$ m away from the base of the tower is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

If a pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground, then sun’s elevation is :

1. (A)$60^{\circ }$
2. (B)$45^{\circ }$
3. (C)$30^{\circ }$
4. (D)$90^{\circ }$