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

11.98

Explanation:

sin 56/11.25 = sin 62/x

Simplifying, this yields the answer x = 11.9814 which rounds to 11.98.

Answer 2

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

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° =
`(perpendicular)/(base)`

Or, Tan 56° =
`(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