45-45-90 Triangles

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The sides opposite the 45° angles are equal, and the hypotenuse is √2 times the length of each leg.

Front

What is the relationship between the legs and the hypotenuse in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if each leg has a length of 'a', then the hypotenuse has a length of 'a√2'.

Front

If one leg of a 45-45-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

How do you find the length of a leg if you know the hypotenuse in a 45-45-90 triangle?

Back

Divide the length of the hypotenuse by √2.

Front

What is the length of each leg in a 45-45-90 triangle with a hypotenuse of 10√2?

Back

Each leg is 10.

Front

If the legs of a 45-45-90 triangle are both 'x', what is the formula for the area of the triangle?

Back

Area = (x^2)/2.

Front

What is the diagonal of a square with side length 's'?

Back

The diagonal is s√2.

Front

If a square has a diagonal of 9√2, what is the length of each side?

Back

Each side is 9.

Front

In a 45-45-90 triangle, what is the ratio of the lengths of the legs to the hypotenuse?

Back

The ratio is 1:1:√2.

Front

What is the value of 'y' if the legs of a 45-45-90 triangle are 11?

Back

y = 11√2.