Special Right triangles

Front

What are the two special right triangles commonly studied in geometry?

Back

The two special right triangles are the 45-45-90 triangle and the 30-60-90 triangle.

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

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

Back

In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2, corresponding to the angles 30°, 60°, and 90°.

Front

If one leg of a 45-45-90 triangle is 10, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 10√2.

Front

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

Back

The length of the longer leg is 5√3.

Front

What is the measure of the angles in a 45-45-90 triangle?

Back

The angles in a 45-45-90 triangle are 45°, 45°, and 90°.

Front

What is the measure of angle A in a 30-60-90 triangle if the longer leg is 10√3?

Back

Angle A is 60°.

Front

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

Back

The length of the hypotenuse is twice the length of the shorter leg.

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the shorter leg?

Back

The length of the shorter leg is 6.

Front

What is the formula for the area of a right triangle?

Back

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