Chapter 9.6, Problem 17E

To determine

Tofind:The unknown length of the triangle.

Answer to Problem 17E

  $x=10$

  $y=10$

Explanation of Solution

Given information:

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

Length of one leg $=x$

Length of second leg $=y$

Length of hypotenuse $=10\sqrt{2}$

Concept Used:

In a ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ right angled triangle, length of both legs are equaland length of hypotenuse is given by product of length of any leg and square root of 2

In a ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ right angled triangle, length of longer leg is product of shorter length and square root of 3 and length of hypotenuse is given by twice the length of shorter leg.

Calculation:

Length of hypotenuse in ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ product of length of any leg and square root of 2

Therefore-

  $\begin{array}{l}10\sqrt{2}=x\sqrt{2}\\ \Rightarrow x=10\end{array}$

Length of both legs in ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ is equal, therefore,

  $\begin{array}{l}y=x\\ \Rightarrow y=10\end{array}$