Chapter 9.6, Problem 2C

To determine

Tofind:The unknown length of the triangle.

Answer to Problem 2C

  $x=9$

  $y=9\sqrt{3}$

Explanation of Solution

Given information:

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

Length of hypotenuse $=18$

Length of shorter leg $=x$

Length of longer leg $=y$

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:

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

Therefore-

  $\begin{array}{l}2x=18\\ \Rightarrow x=\frac{18}{2}\\ \Rightarrow x=9\end{array}$

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

Therefore

  $\begin{array}{l}y=x\sqrt{3}\\ \Rightarrow y=9\sqrt{3}\end{array}$