Question

In ΔABC, m∠A = 90 and if AB : BC = 1:2 find sinB, cosc, tanC.

Answer 1

heya dear friend,
here is your answer

Answer 2

In ∆ABC ,

m<A = 90°

and AB : BC = 1 : 2

Let AB = x , BC = 2x

By Phythogarian theorem ,

BC² = BA² + AC²

=> AC² = BC² - BA²

=> AC² = ( 2x )² - x²

= 4x² - x²

= 3x²

Therefore ,

AC = √3 x

Now ,

i ) SinB= CA/BC

= (√3 x)/2x

= √3/2

Sin B = √3/2

ii ) Cos C = CA/BC

= ( √3 x )/2x

= √3/2

Cos C = √3/2

iii ) tan C = BA/CA

= 1x/(√3 x)

= 1/√3

tan C = 1/√3

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