Question

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

• A. 1, 1
• B. 2, 2
• C. $\frac{1}{\sqrt{2}}$, $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{3}}$, $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is C

$\frac{1}{\sqrt{2}}$, $\frac{1}{\sqrt{2}}$

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