Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a triangle with specific angle measures and side length ratios that make calculations easier. The two main types are the 30-60-90 triangle and the 45-45-90 triangle.

Front

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

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2, where 1 is the length of the side opposite the 30° angle, √3 is the length of the side opposite the 60° angle, and 2 is the hypotenuse.

Front

What is the height of an equilateral triangle with side length 's'?

Back

The height 'h' of an equilateral triangle can be calculated using the formula h = (√3/2) * s.

Front

If the side length of a 30-60-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 8, as it is twice the length of the shorter leg (4).

Front

What is the relationship between the angles in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, both angles are 45°, making it an isosceles triangle with the legs being equal in length.

Front

What are the side length ratios of a 45-45-90 triangle?

Back

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

Front

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

Back

Multiply the length of the shorter leg by √3 to find the length of the longer leg.

Front

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

Back

The area 'A' of a triangle can be calculated using the formula A = (1/2) * base * height.

Front

In a 30-60-90 triangle, if the shorter leg 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 30-60-90 triangle if the hypotenuse is 10?

Back

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