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

Given that, triangle ABC is right angled at B.
So, let $\angle A$ = ${45}^{\circ }$.

We know that,
Sum of all angles of any triangle is ${180}^o$

Now, using the concept of angle sum property of triangle

$\Rightarrow \angle C+{90}^{\circ }+{45}^{\circ }$ = ${180}^{\circ }$

$\Rightarrow \angle C$ = ${180}^{\circ }-{90}^{\circ }-{45}^{\circ }$

$\Rightarrow \angle C$ = ${45}^{\circ }$

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

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