If the height of a tower and the distance of the point of observation from its foot, both are increased by 10%, then the angle of elevation of its top

The kite flying festival in India falls on 14th of January every year marking the arrival of spring and the transaction of the sun into the Makara Rashi (the Capricorn zodiac sign). In quite a few states in India, Makar Sankranti is considered as a major harvest festival. Kite flying on Independence Day in a tradition in North India especially in Delhi, Lucknow Barely and Moradabad.
A kite is flying at a height of 30m from the ground. The length of string from the kite to the ground is 60m. Assuming that there is no stack in the string, the angle of elevation of the kite at ground is

An observer 1.5-metre-tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

The tops of two towers of height x and y, standing on level ground, subtend angles
of 30° and 60° respectively at the centre of the line joining their feet, then find x : y

A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder

If the height of the tower and the shadow is equal then what is angle of
elevation of sun 45º

The angle of depression of an object on the ground from the top of a 25 m
high tower is 30°. Find the distance of the object from the base of the tower.

The angle of depression of a car, standing on the ground, from the top of a 75
m high tower, is 30°.Find the distance of the car from the base of the tower (in m) .

A person is flying a kite at a height of 30 m from horizontal level. The length of
the string is 60 m. Find the angle of elevation of kite.

A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 metres) in height. Answer the following questions (1-5) by seeing the picture. What is the angle of elevation if they are standing at a distance of 42m away from the monument?

They want to see the tower at an angle of 60º. So, they want to know the
distance where they should stand and hence find the distance.

If the altitude of the Sun is at 60º, then the height of the vertical tower that
will cast a shadow of length 20 m is..

The ratio of the length of a rod and its shadow is 1:1. The angle of elevation of
the Sun is

The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is

Assertion: If the shadow of a vertical pole is 1 /√3 of its height, then the altitude of the sun is 60°

Reason: If the sun’s altitude is 45°, then the shadow of a vertical pole is same as its height.

Assertion: The ratio of the length of shadow of a vertical pole to its height is 1: when the sun’s altitude is 60º

Reason: tan 60º = √3

Assertion: If the length of shadow of a vertical pole is equal to its height, then the angle of elevation of the sun is 45º

Reason : According to Pythagoras theorem, h²= l² + b² , where h = hypotenuse, l = length and b = base

If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is
the angle of elevation of the sun?

If the angle of elevation of a tower from a distance of 100 m from its foot is
60°, then what will be the height of the tower?

The length of a string between a kite and a point on the ground is 85 m, if the
string makes an angle θ with the ground level such that tan θ =15 /8 , then at what height is the kite from the ground?
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The angle of depression of a car parked on the road from the top of 150 m high tower is 30°. The distance of the car from the tower (in metres) is

A flag is posted on the top of a castle. A knight on the ground standing 30 m away from the castle notices that the angles of elevation of the top of the castle and the top of the flag are 30° and 45° respectively.How long is the flag?
So length of the flag is s

The upper part of a tree broken over by the wind makes an angle of 30° with the ground and the distance of the root from the point where the top touches the ground is 25 m. What was the total height of the tree?

A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60c to 30c . Find the speed of the boat in metres per minute. .Use√3=1.732

Amit, standing on a horizontal plane, find a bird flying at a distance of 200 m from him at an elevation of 30c. Deepak standing on the roof of a 50 m high building, find the angle of elevation of the same bird to be 45c. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak.

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of a pole of a pole is 60c and the angle of depression from the top of the other pole of point P is .30c Find the heights of the poles and the distance of the point P is 30º from the poles.

(ii) Find the distance PB

(iii) Find the width AB of the river.

Q2. A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate, which is located at the eastern end of the Rajpath, is about 42 metres in height.

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

(ii) They want to see the tower at an angle of 60°. So they want to know  the distance where they should stand and hence the distance is

(iii) If the altitude of Sun is at 60° then the height of the vertical tower
that will cast a shadow of length 20 m, is

Q3. A boy is standing on the top of light house. He observed that boat P and boat Q are approaching to light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. He also knows that height of the light house is 100 m.
Based on the above information, answer the following questions.

(i) Measure of angle ACD isEqual to

Length of CD is equal To

Length of BD is equal To