Given 15 cot A = 8, find sin A and sec A

Solution:

We will use the basic formula of trigonometric ratios cot, sin, and tan to solve the question.

Let us consider a right-angled ΔABC, right-angled at B.

cot A= side adjacent to ∠A / side opposite to ∠A = AB/BC

It is given that 15 cot A = 8

⇒ AB/BC = 8/15

Let AB be 8k. Therefore, BC will be 15 k where k is a positive integer.

Applying Pythagoras theorem in ΔABC, we obtain.

AC² = AB² + BC²

AC² =(8k)² + (15k)²

AC² = 64k² + 225k²

AC² = 289k²

AC = 17k

sin A = side opposite to ∠A / hypotenuse = BC/AC = 15k / 17k = 15/17

sec A = hypotenuse / side adjacent to ∠A = AC/AB = 17k / 8k = 17/8

Thus, sin A = 15/17 and sec A = 17/8.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 8

Video Solution:

Given 15 cot A = 8, find sin A and sec A

Maths NCERT Solutions Class 10 Chapter 8 Exercise 8.1 Question 4

Summary:

If 15 cot A = 8, the value of sin A = 15/17 and sec A = 17/8

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