Chapter 9.6, Problem 11E

To determine

Tofind:The unknown length of the triangle.

Answer to Problem 11E

  $x=10$

  $y=10\sqrt{3}$

Explanation of Solution

Given information:

  ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ right angled triangle

Length of shorter leg $=x$

Length of longer leg $=y$

Length of hypotenuse $=20$

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:

As this is a ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ triangle

Length of hypotenuse is twice the length of shorter leg-

Therefore

  $\begin{array}{l}20=2\left(x\right)\\ \Rightarrow x=\frac{20}{2}\\ \Rightarrow x=10\end{array}$

Length of longer leg is product of shorter length and square root of 3

Therefore

  $\begin{array}{l}y=x\sqrt{3}\\ \Rightarrow y=10\sqrt{3}\end{array}$