Question

Q.13 Given 15cot A = 8, find sin A and sec A​

Answer 1

Answer:

17/8

Explanation:

15 cot A = 8

cot A = 8/15 = base / height

let height be 15x and base be 8x

by pythagoras theorem

(15x)^2 + (8x)^2 = hypotenuse^2

(225+64) × ^2 = hypotenuse^2

17 hypotenuse

Now,

sin A = height / hypotenuse

sin A = 15/17

And,

Sec A = hypotenuse/ base

Sec A = 17/8

Answer 2

Given,

15cotA =8

so, CotA = 8/15

we know that, CotA = b/p

then, Cot A = b/p= 8/15 =BC/AB

Let, consider a right angled triangle ABC in which base BC= 8 and Perpendicular AB = 15

now hypotenuse CA = ?

now, According to Pythagoras theorem we know that

h²=P²+b²

(CA)² =( AB)² + (BC)²

=>(CA)² = 15² + 8²

=> CA =√(225 + 64)

=> CA = √289

=> CA = 17