Question

if 15 cot A= 8,find sin A and sec A.

Answer 1

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Answer 2

Given, 15 cot A = 8

Divide by 15 on both sides,

15 cot A / 15 = 8 / 15

cot A = 8 / 15

we know, cotA = base / height

base / height = 8 / 15

Then, let base = 8 x

let height = 15 x

By Pythagoras Theorem,

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

hypotenuse^2 = ( 225 + 64 )x^2

hypotenuse^2 = 289 x^2

hypotenuse = 17 x

Hence,

sinA = height / hypotenuse

sin A = 15 x / 17 x

sin A = 15 / 17

secA = hypotenuse / base

sec A = 17 x / 8 x

sec A = 17 / 8