Calculate 30-60-90 triangle long leg 5√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 5√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 = 5√3.

x√3 = 5√3

Careful!

Half is only for the hypotenuse.

The long leg is x times √3.

Careful: not x = 5√3 ÷ 2 ✗

Both sides are times √3.

So x = 5.

x = 5

3 Find the hypotenuse

The hypotenuse is 2x: 2 times 5.

hypotenuse = 2 × 5

So the hypotenuse is 10.

hypotenuse = 10

So the short leg is 5 and the hypotenuse is 10.

short leg 5 and hypotenuse 10

4 Check

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

5² + (5√3)² = 25 + 25 × 3 = 25 + 75 = 100

The hypotenuse squared: 10² is 100.

10² = 100

Both are 100.

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