Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios, such as the 45-45-90 triangle and the 30-60-90 triangle.

Front

What is the ratio of the sides in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the sides are in the ratio 1:1:√2.

Front

What is the ratio of the sides in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2.

Front

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

Back

The length of the hypotenuse is x√2.

Front

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

Back

The length of the longer leg is x√3.

Front

If the hypotenuse of a 30-60-90 triangle is '2x', what is the length of the shorter leg?

Back

The length of the shorter leg is x.

Front

What is the formula to find the area of a triangle?

Back

The area of a triangle is given by the formula: Area = (1/2) * base * height.

Front

In a 45-45-90 triangle, if one leg is 8, what is the length of the hypotenuse?

Back

The hypotenuse is 8√2.

Front

In a 30-60-90 triangle, if the shorter leg is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 10.

Front

What is the perimeter of a 45-45-90 triangle with legs of length 10?

Back

The perimeter is 10 + 10 + 10√2 = 20 + 10√2.