Q. 34.3( 240 Votes )

# If sin  calculate Cos A and tan A

Let ΔABC be a right-angled triangle, right-angled at point B

Given that:

As we know trigonometrical ratios give ratio between sides of right angled triangle instead of their actual values. So from sin A we get the ratio of Perpendicular and Hypotenuse of the triangle. Now as we don't know the exact value let Perpendicular = 3 k and Hypotenuse = 4 k

According to Pythagoras theorem: (Hypotenuse)2 = (Base)2 + (Perpendicular)2

Applying Pythagoras theorem in ΔABC, we obtain

AC2 = AB2 + BC2

(4k)2 = AB2 + (3k)2

16k2 - 9k2 = AB2

7k2 = AB2

Cos A =

= =

And we know that

Tan A =

= =

So the ratios are cos A = √7/4 and tan A = 3/√7

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