Question

5. If, 15 cot A-8, then find the value of tan A? in questions. ​

Answer 1

Step-by-step explanation:

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.