Question

In triangle ABC, right angled at B, if one angle is ${45}^{\circ }$, find the value of sin A and cos C.

Answer 1

In right angle triangle ABC, $\angle B$ = ${90}^{\circ }$.

Let $\angle A$ = ${45}^{\circ }$.

Then $\angle C$ = ${180}^{\circ }-{90}^{\circ }-{45}^{\circ }$ = ${45}^{\circ }$ (using angle sum property)

So, sin A = sin ${45}^{\circ }$ = $\frac{1}{\sqrt{2}}$

and cos C = cos ${45}^{\circ }$ = $\frac{1}{\sqrt{2}}$