Chapter 9.6, Problem 9E

To determine

Tofind:The unknown length of the triangle.

Answer to Problem 9E

  $x=5$

  $y=5\sqrt{2}$

Explanation of Solution

Given information:

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

Length of one leg $=5$

Length of second leg $=x$

Length of hypotenuse $=y$

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

  $x=5$

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

Therefore-

  $y=5\sqrt{2}$