Chapter 9.6, Problem 30E

To determine

Tofind:The unknown length of the triangle.

Answer to Problem 30E

  $x=12\sqrt{3}$

Explanation of Solution

Given information:

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

Length of hypotenuse $=24\text{ ft}$

Length of longer leg $=x$

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:

Let length of shorter leg be $y$

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

Therefore-

  $\begin{array}{l}24=2\left(y\right)\\ \Rightarrow y=12\end{array}$

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

Therefore

  $\begin{array}{l}x=y\sqrt{3}\\ \Rightarrow x=12\sqrt{3}\end{array}$