Question
In a $\triangle\text{ABC}, \angle\text{B}= 35^\circ$ and $\angle\text{C}= 55^\circ$. Write which of the following is true:
i. $AC^2=AB^2+BC^2$
ii. $A B^2=B C^2+A C^2$
iii. $B C^2=A B^2+A C^2$

Answer



$\text { In } \triangle \mathrm{ABC} \text {, }$
$\angle \mathrm{B}=35^{\circ} \text { and } \angle \mathrm{C}=55^{\circ}$
$\Rightarrow \angle \mathrm{A}=180^{\circ}-(\angle \mathrm{B}+\angle \mathrm{C})$
$\Rightarrow \angle \mathrm{A}=180^{\circ}-\left(35^{\circ}+55^{\circ}\right)$
$\Rightarrow \angle \mathrm{A}=180^{\circ}-90^{\circ}$
$\angle \mathrm{A}=90^{\circ}$
By Pythagoras Theorem,
$\mathrm{BC}^2=\mathrm{A}\mathrm{B}^2+\mathrm{AC}^2$
$(iii)$ is true.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free