Question

An isosceles triangle used to rack billiard balls has a base of 11.25 inches. The sides of the triangle meet at a 56° angle. To the nearest hundredth what is the length of each side?

Answer 1

Answer:

The measure of each sides of isosceles triangle is 16.67 inches , 16.67 inches , 11.25 inches

Step-by-step explanation:

Given as for a Isosceles triangle :

The base of Triangle = 11.25 inches

The sides of triangle meets at 56°

Let the unknown side measure = x inches

From The property of isosceles triangle

The angle opposite to the same side are equal

I.e $\Theta _1$ =  $\Theta _2$ = 56°

So, The third angle = 180° - ( $\Theta _1$ +  $\Theta _2$ )

Or, The third angle = 180° - ( 56° + 56° )

∴   The third angle = 180° - 112° = 68°

Now, From isosceles triangle

Tan 56° = $\frac{perpendicular}{base}$

Or, Tan 56° = $\frac{x}{11.25}$

∴   x = 11.25 × Tan 56°

Or, x = 11.25 × 1.482 = 16.672 inches

Hence The measure of each sides of isosceles triangle is 16.67 inches , 16.67 inches , 11.25 inches   Answer