Calculate 30-60-90 triangle long leg 12√3 Step by Step

Step by step

The question

Question: find the other two sides of a 30-60-90 triangle with a long leg of 12√3.

1 Half of an equilateral

The angles are 30°, 60° and 90°.

Put a copy under it, upside down.

Together they make a triangle with three equal sides.

That is an equilateral triangle.

All three sides are equal, and every angle is 60°.

The short leg is across from the 30° angle.

It is half of one side.

We call it x.

The other half of that side is x too.

The hypotenuse is one whole side.

So it is 2 times the short leg.

The long leg is the short leg times √3.

2 Find the short leg

The long leg is x√3.

So x√3 = 12√3.

x√3 = 12√3

Careful!

Half is only for the hypotenuse.

The long leg is x times √3.

Careful: not x = 12√3 ÷ 2 ✗

Both sides are times √3.

So x = 12.

x = 12

3 Find the hypotenuse

The hypotenuse is 2x: 2 times 12.

hypotenuse = 2 × 12

So the hypotenuse is 24.

hypotenuse = 24

So the short leg is 12 and the hypotenuse is 24.

short leg 12 and hypotenuse 24

4 Check

Let's check with Pythagoras: short leg squared plus long leg squared.

12² + (12√3)² = 144 + 144 × 3

= 144 + 432 = 576

The hypotenuse squared: 24² is 576.

24² = 576

Both are 576.

So the sides are right!

Let's look back.

First: half of an equilateral.

Then: find the short leg.

Then: find the hypotenuse.

Last: check.

Answer