Chapter 9, Problem 6CST

To determine

Tofind:The unknown length of the triangle.

Answer to Problem 6CST

  $18.3847\text{ yards}$

Explanation of Solution

Given information:

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

Length of leg $=13\text{ yards}$

Concept Used:

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

Let length of hypotenuse be $x$

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

Therefore-

  $\begin{array}{l}x=13\sqrt{2}\\ \Rightarrow x=13\left(1.4142\right)\\ \Rightarrow x=18.3847\text{ yards}\end{array}$