This is a Triangle.

A triangle has three sides.

This is a right triangle.

A right triangle has 2 legs, one hypotenuse, and an angle of 90°

The hypotenuse is ALWAYS the longest part of a right triangle.

The legs always have the same or different lengths depending on the type of right triangle.

Sometimes we don't know one of the legs or the hypotenuse.

?

The Pythagorean theorem can be used to find this. All it takes is a few simple steps.

The Pythagorean theorem states;

a ² + b ² = c ² 

A RESCUE STORY

Nick city has the best fireman in the city. He's known as fireman Sam and together with his team he stops houses from burning, saves cats from trees, and stray animals too.

Fireman Sam and his team receive a call at the fire station; a house was on fire somewhere in the city.

They get there but to put out the fire they need to know how long the ladder must be to put out the fire on the burning roof.

Fireman Sam must figure this out quickly before the whole building burns down.

How long will the ladder be?

Whoa! That makes a right triangle! He can definitely solve this by using the Pythagorean Theorem.

He knows the 2 legs,but not the hypotenuse.

The formula for the Pythagorean states a² + b² = c², and to find the length of the ladder he:

1) Identifies the unknown part and the given parts.

2) Set up the equation:

• 16² + 4² = x²

3) Solve for the unknown

• 16² + 4² = x²
• (16*16)+(4*4)= x²
• 256 + 16=x²
• x² = 272
• x=
• x=16.5 ft

A- Leg (16 ft)

B- Leg (4 ft)

C- Hypotenuse (x)

272

16 ft

Fireman Sam figured out how long the ladder needs to be...

4 ft

16.5 ft

...and with the help of everyone on his team, he puts out the fire.

Once again, Fireman Sam and his team have saved the day.

What happens if we don't know one of the legs?