Question

If a triangle has angles ${45}^{\circ },{45}^{\circ }$, and ${90}^{\circ }$, what is the value of AB when AC = $14\sqrt{2}$ m ?

• A. 11 m
• B. 16 m
• C. 14 m
• D. 24 m

Answer 1

The correct option is C 14 m

We have theorem :

" If the angles of a triangle are ${45}^{\circ },{45}^{\circ }$, and ${90}^{\circ }$,then each of the perpendicular sides is $\frac{1}{\sqrt{2}}$ times the hypotenuse " .

AC= hypotenuse = $14\sqrt{2}$ m .


So, AB = $\frac{1}{\sqrt{2}}\times 14\sqrt{2}=14m$