Introduction to Trigonometry Exercise 8.1
NCERT solutions for Maths Introduction to Trigonometry
NCERT Solutions for Class 10 Maths Introduction to Trigonometry
1. In 
ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine:
(i) 
(ii) 
Ans. Let us draw a right angled triangle ABC, right angled at B.
Using Pythagoras theorem,
= 
= 576 + 49 = 625
AC = 25 cm
(i) 
, 
(ii) 
, 
2. In adjoining figure, find 
:
Ans. Using Pythagoras theorem,
=169 – 144 = 25
QR = 5 cm
= 
= 
= 0
NCERT Solutions for Class 10 Maths Exercise 8.1
3. If 
calculate 
and 
Ans. Given: A triangle ABC in which 
B = 
Let BC = 
and AC = 
Then, Using Pythagoras theorem,
AB = 
= 
= 
= 
NCERT Solutions for Class 10 Maths Exercise 8.1
4. Given 
find 
and 
Ans. Given: A triangle ABC in which B =
Let AB = 
and BC = 
Then using Pythagoras theorem,
AC = 
= 
= 
= 
= 
NCERT Solutions for Class 10 Maths Exercise 8.1
5. Given 
calculate all other trigonometric ratios.
Ans. Consider a triangle ABC in which A = 
and B =
Let AB = 
and BC = 
Then, using Pythagoras theorem,
BC = 
= 
= 
= 
=
NCERT Solutions for Class 10 Maths Exercise 8.1
6. If And B are acute angles such that 
then show that A = B.
Ans. In right triangle ABC,
and 
But 
[Given]
AC = BC
A = B
[Angles opposite to equal sides are equal]
NCERT Solutions for Class 10 Maths Exercise 8.1
7. If 
evaluate:
(i) 
(ii) 
Ans. Consider a triangle ABC in which A = and B =
Let AB = 
and BC =
Then, using Pythagoras theorem,
AC = 
= 
= 
= 
= 
(i) = 
= 
= 
= 
(ii) 
= 
=
NCERT Solutions for Class 10 Maths Exercise 8.1
8. If 
check whether 
or not.
Ans. Consider a triangle ABC in which B = .
And 
Let AB = and BC = 
Then, using Pythagoras theorem,
AC =
= 
= 
= =
And 
Now, L.H.S. 
= 
= 
= 
R.H.S. 
= 
= 
=
L.H.S. = R.H.S.
=
NCERT Solutions for Class 10 Maths Exercise 8.1
9. In ABC right angles at B, if 
find value of:
(i) 
(ii) 
Ans. Consider a triangle ABC in which B = .
Let BC = 
and AB = 
Then, using Pythagoras theorem,
AC =
= 
= 
= 
= 
For C, Base = BC, Perpendicular = AB and Hypotenuse = AC
(i) = 
= 
= 1
(ii) = 
= 
NCERT Solutions for Class 10 Maths Exercise 8.1
10. In PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of nd 
Ans. In PQR, right angled at Q.
PR + QR = 25 cm and PQ = 5 cm
Let QR = 
cm and PR = 
cm
Using Pythagoras theorem,
RQ = 12 cm and RP = 25 – 12 = 13 cm
And 
NCERT Solutions for Class 10 Maths Exercise 8.1
11. State whether the following are true or false. Justify your answer.
(i) The value of 
is always less than 1.
(ii) 
for some value of angle A.
(iii) is the abbreviation used for the cosecant of angle A.
(iv) 
is the product of 
and A.
(v) 
for some angle 
Ans. (i) False because sides of a right triangle may have any length, so may have any value.
(ii)True as 
is always greater than 1.
(iii) False as is the abbreviation of cosine A.
(iv) False as is not the product of ‘cot’ and A. ‘cot’ is separated from A has no meaning.
(v) False as 
cannot be > 1.