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.

 Case Study ‐ 07
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.

1. What is the angle of elevation if they are standing at a distance of 42m away from the monument?

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

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

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

Soln:

1. What is the angle of elevation if they are standing at a

distance of 42m away from the monument?

Look at the diagram.

Here AB is the height of India Gate

And BC is the distance between students and

India Gate

Here we want to find the angle of Elevation .

Given that,

AB 􀵌 42 m

BC 􀵌 42 m

Now find the tan

tan􀟠 􀵌 􀯈􀯣􀯣􀯢􀯦􀯜􀯧􀯘 􀯦􀯜􀯗􀯘

􀮺􀯗􀯝􀯔􀯖􀯘􀯡􀯧 􀯌􀯜􀯗􀯘

􀵌 􀬸􀬶

􀬸􀬶 􀵌 1

tan  􀵌 1

  􀵌 450

Hence Angle of elevation is 450.

􁈺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 find the

distance

Soln:

In this case, the students see the tower at

an angle of 600. So we need to find the

distance between India gate and students.

Given that

Height of India Gate 􀵌 42 m

Angle 􀵌 600

Let the distance be x m

Now, find the tan 

tan􀟠􀵌􀯈􀯣􀯣􀯢􀯦􀯜􀯧􀯘

􀮺􀯗􀯝􀯔􀯖􀯘􀯡􀯧

tan60􀵌􀮺􀮻

􀮻􀮼

√3 􀵌 􀬸􀬶

􀯫

3 x 􀵌 42

x 􀵌 42/3

Multiply numerator and denominator by 3, we get

x 􀵌 􀬸􀬶√􀬷

􀬷 􀵌 143

Solving we get

x 􀵌 25.24 m

Hence, the distance between India Gate and Students is 25.24 m

􁈺iii􁈻 If the altitude of the Sun is at 60 , then the height of the

vertical tower that will cast a shadow of length 20 m is

Soln:

This diagram illustrate the problem.

Let the height of tower 􀵌 h m

Length of shadow 􀵌 20 m.

Angle 􀵌 600

Now find tan 

tan􀟠􀵌􀮺􀮻

􀮻􀮼

tan60􀵌 􀯛

􀬶􀬴

√3 􀵌 􀯛

􀬶􀬴

h 􀵌 20 3

Solving we get

h 􀵌 34.6 m

Hence the height of the tower is 34.6 m or 203 m

􁈺iv􁈻 The ratio of the length of a rod and its shadow is 1:1 .

Find the angle of elevation of the Sun

Soln:

Let AB is the length of rod and

BC is the length of the shadow

It is given that length of rod and its

shadow is 1: 1, that means AB 􀵌 BC.

Here the rod is vertical and shadow is horizontal, we can

form a right angle triangle, shown in the figure.

We need to find the angle of elevation.

So, find tan 

tan􀟠􀵌􀮺􀮻

􀮺􀮼

tan􀟠􀵌􀮺􀮻

􀮺􀮻 􀵌 1

tan  􀵌 1

  􀵌 450

Hence the angle of elevation is 450.