Question

In right triangle abc, when angles a and b add up to 90 degrees, what is the cosine of b equal to

Answer 1

In that case, cosine of b = sine of a.

Answer 2

cos B = sin A

Explanation:

Given: Δ ABC is a right angles triangle

m∠A + m∠B = 90°

To find: Cos B equals to

Figure is attached.

Using trigonometric ratios in Δ ABC,

We get,

`cos\,B\,=\,(base)/(hypotenuse)\,=\,(CB)/(AB)`

`sin\,B\,=\,(altitude)/(hypotenuse)\,=\,(AC)/(AB)`

`cos\,A\,=\,(altitude)/(hypotenuse)\,=\,(AC)/(AB)`

`sin\,B\,=\,(base)/(hypotenuse)\,=\,(CB)/(AB)`

So, From above it is clear

cos B = sin A

Therefore, cos B = sin A