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