Class 10 MAHARASHTRA STATE TEXTBOOK BUREAU Solutions Maths Chapter 6 - Trigonometry
Trigonometry Exercise 6.1
Solution 1
Given:
We have to find
the values of 
As we know,
Also,
Thus,
.
Solution 2
Given:
We have to find
the values of 
As we know,
And,
Thus,
.
Solution 3
Given:
We have to find
values of 
As we know,
And,
Thus, 
.
Solution 4
Given:
We have to find
the values of 
Assuming the constant of the ratios as 'k', we have the triangle,
Solution 5
Given 
We have to find
the value of 
It is given that
This is possible
when 
Thus, 
.
Solution 6(i)
We have to prove 
First, we simplify LHS
As, LHS=RHS
Hence, 
is
proved.
Solution 6(ii)
We have to prove 
First, we simplify LHS
As, LHS=RHS
Hence, is
proved.
Solution 6(iii)
We have to prove 
First, we simplify LHS
As, LHS=RHS
Hence, 
is
proved.
Solution 6(iv)
We have to prove 
First, we simplify LHS
As, LHS=RHS
Hence, 
is
proved.
Solution 6(v)
We have to prove 
First, we simplify LHS
As, LHS=RHS
Hence, 
is
proved.
Solution 6(vi)
We have to prove 
First, we simplify LHS
As, LHS=RHS
Hence, 
is
proved.
Solution 6(vii)
We have to prove 
First, we simplify LHS
As, LHS=RHS
Hence, 
is
proved.
Solution 6(viii)
We have to prove 
First, we simplify LHS
Now, we simplify RHS,
As, LHS=RHS
Hence, is
proved.
Solution 6(ix)
Given: 
…….
(i)
We have to show 
Squaring the given equation (i),
Hence proved.
Solution 6(x)
We have to prove 
(NOTE:
The question
should be
(
in
RHS))
First, we simplify LHS
As, LHS=RHS
Hence, 
is
proved.
Solution 6(xi)
We have to prove 
First, we simplify LHS
RHS
=1
As, LHS=RHS
Hence, 
is
proved.
Solution 6(xii)
We have to prove 
First, we simplify LHS
Now simplifying
RHS
As, LHS=RHS
Hence, 
is
proved.
Trigonometry Exercise 6.2
Solution 1
Given,
Distance between person and the
church 
Angle of elevation 
Let the height of the church be 
The height of the church is 80 m.
Solution 2
Given,
The angle of
depression, 
Height of
lighthouse, 
Let the distance of ship from lighthouse be d,
The ship is 51.96 m away from the lighthouse.
Solution 3
Given,
Width of the
road, 
Height of 1st
building, 
Angle of
elevation,
Let the height of
the second building, be 
Such that 
The height of the second building is 30.78m.
Solution 4
Given,
Height of poles
Length of wire, 
Let us divide the 18m pole in two parts a and b.
From the above figure we get,
We have to find the angle made by the wire with horizontal
Solution 5
Given,
Distance
between the base and treetop 
Angle
with horizontal 
We have to find the height of the tree H
Height of tree is 74.6m.
Solution 6
Given,
Height of kite is 60m
Angle with ground is 60°
We have to find the length of the string.
Length of the string
Length of the string is 69.2m.
Trigonometry Exercise Problem Set 6
Solution 1(i)
We have to find the value of 
The correct option is (A) 1.
Solution 1(ii)
We have to find the value of 
The correct option is (B)
.
Solution 1(iii)
We have to find the value of 
The correct option is (C)
.
Solution 1(iv)
When we see at a higher level, from the horizontal line, the angle formed is Angle of elevation.
is the angle of elevation
The correct option is (A) Angle of elevation.
Solution 2
Given,
Trigonometric identity is
Thus,
Solution 3
Given:
We have to find:
If
Solution 4
Given:
We have to find:
If
Solution 5(i)
We have to prove
RHS
=1
LHS=RHS
Hence proved.
Solution 5(ii)
We have to prove
RHS
=
LHS=RHS
Hence proved.
Solution 5(iii)
We have to prove
LHS=RHS
Hence proved.
Solution 5(iv)
We have to prove,
LHS=RHS
Hence proved.
Solution 5(v)
We have to prove
LHS=RHS
Hence proved.
Solution 5(vi)
We have to prove
LHS=RHS
Hence proved.
Solution 5(vii)
We have to prove
LHS=RHS
Hence proved.
Solution 5(viii)
We have to prove 
LHS=RHS
Hence proved.
Solution 5(ix)
We have to prove 
LHS=RHS
Hence proved.
Solution 5(x)
We have to prove 
LHS=RHS
Hence proved.
Solution 6
Given,
Distance from the
building, 
Angle of
elevation, 
Height of the
building is 
.
Solution 7
Given,
Light
of the lighthouse, 
Angle
of depression, 
Ship
is 
away
from the lighthouse.
Solution 8
Given,
Width of the road is 15m
Height of first building 12m
Angle of the elevation is 30°
From the diagram we can see
Thus, the height of the second building,
Height
of the second building is 
m.
Solution 9
Given,
Angle
of elevation 
Length of ladder is 20m
Height of platform is 2m
Thus, the height from the ground up to which ladder can reach is 20.8m.
Solution 10
Given,
Angle of depression is 20°
Speed of plane 200 km/hr
Time to reach ground after 54s
Height at which the plane was when it started landing is 0.972km.
