CUET General Test Geometry > Trigonometry PYQs

Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 meters, find the distance between the two men.

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°. Determine the height of the chimney?

The angle of elevation of the top of a tower from a certain point is 60°. If the observer moves 10 m away from the tower, the angle of elevation of the top of the tower decreases by 15°. The height of the tower is:

From the top of a tower, the angles of depression of two objects A and B (situated on the ground on the same side of the tower) are observed to be 30° and 60°, respectively. If the distance between the objects is 200√3 m, then the height of the tower is?

The shadow of the pole standing on a level surface is found to be 5 m shorter when the sun's elevation is 60° than when it is 45°. What is the height of the pole?

A 2 m tall boy is 30 m away from a tower. The angle of elevation of the top of the tower from his eye is 45°. What is the height of the tower?

From the top of a building 78 m high, the angles of depression of the bottom and the top of a tower are observed to be 45° and 30° respectively. Determine the approximate height of the tower so observed?

The tops of two poles of height 38 m and 56 m are connected by a cable. If the cable makes an angle of 30° with the horizontal, then the distance between the bases of the poles is:

The tops of two poles of height 22 m and 31 m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire (in m) is:

The angle of elevation of the sun, when the length of the shadow of a tower is 1/√3 times the height of the tower, is

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

If the height of a pole is $8\sqrt{3}$ meters and the length of its shadow is 8 meters, then the angle of elevation of the sun is:

The tops of two poles of height 25 m and 16 m are connected by a wire. If the wire makes an angle 30° with the vertical, then the distance between the two poles is

At the foot of a mountain, the elevation of the summit is 45°. After ascending 2 kilometers towards the mountain, at an incline of 30°, the elevation changes to 60°. Determine the height of the mountain?

The angle of elevation of the top of an unfinished tower at a distance of 75m from its base is 30°. How much higher must the tower be raised so that the angle of elevation of its top at the same point may be 60°?

A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 60° with the man's eye when at a distance of 60 metres from the tower. After 9 seconds, the angle of depression becomes 30°. The speed of the boat, assuming that it is running in still water, will be:

From a point exactly midway between the foot of two towers P and Q, the angle of elevation of their tops are 30° and 60°, respectively. The ratio of the heights of tower P to that of Q is:

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower when seen from the foot of the building is 60°. If the tower is 60 m high, then the height of the building is:

The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it is 60°. Find the height of the tower.

From A point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 9 m from the surface of the river, then find the width of the river.

An observer 2 m tall is 24$\sqrt{3}$ m away from a building. The angle of elevation of the top of the building as seen by him is 30°. What is the height of the building?

The angles of elevation of the top of a tower from two points at a distance of 5 meters and 20 meters along the same straight line from the base of the tower, are complementary. Find the height of the tower.

If $\sin A = \frac45$, then $(3 - \tan A) (2 + \cos A) =$

The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree is :

A man standing on the bank of a river observes that the angle subtended by a tree standing on the opposite bank is 60 degrees on his side of bank. When he moved away 24m from the bank, he finds the angle to be 30 degrees. Find the breadth of the river:

From a point P on the ground the angle of elevation of the top of 10 m high building is $30°$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from the point P is $45°$. Length of the flagstaff is: (Take $\sqrt{3} = 1.732$)

In a $\Delta ABC$ right angled at A, if $\angle ABC = 60^\circ$ and AC = 4 units, then length of BC (in units) is :

In a triangle ABC right angled at B, AB=8 unit and AC=10 unit. What is the value of $\sin^2\theta - \cos^2\theta$ where theta is angle ACB ?

If in $\triangle ABC$ $\angle A + \angle B = 90^\circ$ and $\sin B = \frac{4}{5}$, then find the value of $\cos A$.

If $\sin\theta + \csc\theta = 2$, then what is the value of $\sin^2\theta + \csc^2\theta$?

If $\sin 2\theta = \cos 40^\circ$, then the smallest positive value of $\theta$ is :

If $3\sin\theta - 4\cos\theta = 0$, then value of $\tan\theta\cdot\csc\theta$ is :

In $\triangle ABC$ with AB = 5 cm, BC = 12 cm, AC = 13 cm and $\angle B = 90^\circ$, which of the following is/are not correct? (a) $\tan C = \frac{12}{13}$ (b) $\text{cosec} A = \frac{13}{12}$ (c) $\sin B = \frac{5}{13}$ (d) $\tan A = \frac{12}{15}$ (e) $\cos C = \frac{12}{13}$ Choose the correct answer from the options given below:

Find the angle of elevation of the Sun, when the length of the shadow of a tree is $\frac{1}{\sqrt{3}}$ times the height of the tree.

Find the angle of elevation of the Sun, when the length of the shadow of a tree is $\frac{1}{\sqrt{3}}$ times the height of the tree.

If the height of tree is $3\sqrt{3}$ meters and length of its shadow is 3 meters. Find the angle of elevation of the sun.

The angle of depression of a point situated at a distance 100 m from the base of a pole is 30 degrees. Find height of the pole is-

The angle of depression of a point situated at a distance 500 m from the base of tower is $45°$. The height of tower is _____.