30-60-90 and 45-45-90 Triangles

Front

What is a 30-60-90 triangle?

Back

A right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides opposite these angles are in the ratio 1:√3:2.

Front

What is a 45-45-90 triangle?

Back

A right triangle where the angles are both 45 degrees and the sides opposite these angles are equal. The ratio of the sides is 1:1:√2.

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle?

Back

The hypotenuse is twice the length of the shorter leg (opposite the 30-degree angle).

Front

How do you find the length of the longer leg in a 30-60-90 triangle?

Back

The longer leg (opposite the 60-degree angle) is √3 times the length of the shorter leg.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

If the shorter leg of a 30-60-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 8.

Front

If the legs of a 45-45-90 triangle are each 5, what is the length of the hypotenuse?

Back

The hypotenuse is 5√2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

The lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do you solve for x in a 30-60-90 triangle if you know the longer leg?

Back

Divide the length of the longer leg by √3 to find the shorter leg, then multiply by 2 to find the hypotenuse.

Front

What is the value of x if the shorter leg of a 30-60-90 triangle is 3?

Back

x (hypotenuse) = 6.