Special Right 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 a 30°-60°-90° triangle?

Back

A special right triangle where the angles are 30°, 60°, and 90°. The side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

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

Back

In a 45°-45°-90° triangle, if each leg is 'x', then the hypotenuse is 'x√2'.

Front

What is the relationship between the sides of a 30°-60°-90° triangle?

Back

In a 30°-60°-90° triangle, if the shorter leg (opposite the 30° angle) is 'x', then the longer leg (opposite the 60° angle) is 'x√3' and the hypotenuse is '2x'.

Front

If the legs of a 45°-45°-90° triangle are 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

If the shorter leg of a 30°-60°-90° triangle is 5, what is the length of the longer leg?

Back

The longer leg is 5√3.

Front

What is the value of x in a 45°-45°-90° triangle if the hypotenuse is 8√2?

Back

x = 8.

Front

What is the value of y in a 30°-60°-90° triangle if the hypotenuse is 10?

Back

y = 5√3.

Front

What is the area of a 45°-45°-90° triangle with legs of length 6?

Back

Area = (6 * 6) / 2 = 18.

Front

What is the perimeter of a 30°-60°-90° triangle with a shorter leg of 3?

Back

Perimeter = 3 + 3√3 + 6 = 3 + 3√3 + 6.