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 :

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 [tex]\Theta _1[/tex] =  [tex]\Theta _2[/tex] = 56°

So, The third angle = 180° - ( [tex]\Theta _1[/tex] +  [tex]\Theta _2[/tex] )

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

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

Now, From isosceles triangle

Tan 56° = [tex]\frac{perpendicular}{base}[/tex]

Or, Tan 56° = [tex]\frac{x}{11.25}[/tex]

∴   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

Answer:

11.98

Step-by-step explanation:

sin 56/11.25 = sin 62/x

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

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