Chapter 9.6, Problem 1C

To determine

Tofind:The unknown length of the triangle.

Answer to Problem 1C

  $x=7\sqrt{2},y=7$

Explanation of Solution

Given information:

  ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ right angled triangle

Length of one leg- $a=7$

Concept Used:

In a ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ right angled triangle, length of both legs are equal say $a$ and length of hypotenuse is given by $a\sqrt{2}$

In a ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ right angled triangle, with shorter leg of length $a$ , length of longer leg will be given by $a\sqrt{3}$ and length of hypotenuse is given by $2a$

Calculation:

As length of both legs are equal in ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ right angled triangle,

Length of second leg will be- $y=a=7$

Length of hypotenuse will be-

  $\begin{array}{l}x=a\sqrt{2}\\ =7\sqrt{2}\end{array}$