Special Right Triangles

Front

What are the properties of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the legs are congruent, 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

The ratio of the sides in a 30-60-90 triangle is 1:√3:2, where 1 is the length of the shorter leg, √3 is the length of the longer leg, and 2 is the length of the hypotenuse.

Front

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

Back

Multiply the length of the leg by √2 to find the length of the hypotenuse.

Front

If the hypotenuse of a 30-60-90 triangle is 10, what are the lengths of the legs?

Back

The shorter leg is 5, and the longer leg is 5√3.

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

Back

The hypotenuse is 8.

Front

What is the relationship between the angles and sides in a right triangle?

Back

In a right triangle, the side opposite the largest angle (90 degrees) is the hypotenuse, and the other two sides are the legs.

Front

How can you determine the length of the longer leg in a 30-60-90 triangle?

Back

The length of the longer leg is √3 times the length of the shorter leg.

Front

What is the significance of special right triangles in geometry?

Back

Special right triangles provide specific ratios and relationships that simplify calculations in trigonometry and geometry.

Front

If one leg of a 45-45-90 triangle is 7, what is the length of the hypotenuse?

Back

The hypotenuse is 7√2.