CUET General Test: GeometryTrigonometry. Free, no login required.

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 _____.