Question

If $\Delta ABC$ is a right triangle such that $\angle C={90}^{\circ },\angle A={45}^{\circ }$ and $BC=7$ units. Find $\angle B,AB$ and $AC$.

Answer 1

$△ABC$ is $rightangled$ at $C$

$\angle C={90}^{\circ },\angle A={45}^{\circ }$

We know that,

In triangle $ABC$, $\angle A+\angle B+\angle C={180}^{\circ }$

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

$\angle B={45}^{\circ }$

It's a scalene triangle.

$\therefore BC=AC=7units$

From Pythagoras theorem,

$A{B}^2=A{C}^2+B{C}^2$

$A{B}^2=7^2+7^2=98$

$AB=7\sqrt{2}$