Chapter 9, Problem 30CR

To determine

Tofind:The $x$ and $y$

Answer to Problem 30CR

  $y=8$

  $x=4\sqrt{3}$

Explanation of Solution

Given information:

Concept Used:

In a ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ right angled triangle, length of both legs isequal,and 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:

We know,

Length of hypotenuse in ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ is twice the length of shorter leg

Therefore-

  $\begin{array}{l}y=2\left(4\right)\\ y=8\end{array}$

Length of longer leg in ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ is product of shorter leg length and square root of 3

  $x=4\sqrt{3}$