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
⇒ AC² = AB² + BC²
⇒ AC² = 24² + 7²
⇒ AC² = 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,
PR² = PQ² + QR² ……..(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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