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

Front

What are the side lengths of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2. The shorter leg (opposite the 30° angle) is 'x', the longer leg (opposite the 60° angle) is 'x√3', and the hypotenuse (opposite the 90° angle) is '2x'.

Front

How do you find the longer leg in a 30-60-90 triangle if the short leg is known?

Back

To find the longer leg, multiply the length of the short leg by √3.

Front

What is the approximate decimal value of √3?

Back

The approximate decimal value of √3 is about 1.732.

Front

What are the side lengths of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1 : 1 : √2. Both legs are equal, and the hypotenuse is '√2' times the length of each leg.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

To find the hypotenuse, multiply the length of one leg by √2.

Front

If the leg of a 45-45-90 triangle is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 5√2.

Front

What is the value of 4√3 in decimal form?

Back

4√3 is approximately 6.928.

Front

If the short leg of a 30-60-90 triangle is 9, what is the longer leg?

Back

The longer leg is 9√3.

Front

What is the relationship between the angles and sides in a 30-60-90 triangle?

Back

The angles are 30°, 60°, and 90°, and the sides are in the ratio 1 : √3 : 2.

Front

If a leg of a 45-45-90 triangle is 'a', what is the length of the other leg?

Back

The other leg is also 'a' since both legs are equal.