# Gujarat Board Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1

Gujarat Board Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1

## Gujarat Board Textbook Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1

Question 1.

In ΔABC, right angled at B, AB = 24 cm, BC = 7 cm, determine

(i) sin A, cos A

(ii) sin C, cos C

Solution:

We have

AB = 24 cm

BC = 7 cm

(i) In right ΔABC

⇒ AC^{2} = AB^{2} + BC^{2}

⇒ AC^{2} = 24^{2} + 7^{2}

⇒ AC^{2} = 576 + 49

Question 10.

In APQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the value of sin P, cos P and tan P.

Solution:

In right triangle PQR,

PR^{2} = PQ^{2} + QR^{2} ……..(1)

(By Pythagoras theorem)

PR + QR = 25

⇒ PR = 25 – QR ……….(2)

Question 11.

State whether the following are true or false. Justify your answer.

(i) The value of tan A is always less than 1

(ii) sec A = 12/5 for some value of A

(iii) cos A is the abbreviation used for the cosecant of angle A

(iv) cot A is the product of cot and A

(v) sin θ = 4/3 for some angle.

Solution:

(i) False.

the value of the perpendicular may be longer than the base.

(ii) True

Because Hypotenuse is always greater than the base.

(iii) False

Since cos A is the abbreviation used for the cosine of angle A.

(iv) False

Since cot is meaningless without angle A.

(v) False

Since value of sin O is always less than 1.

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