Special Right Triangles A

Front

What is a special right triangle?

Back

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

Front

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

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1:1:√2. This means if each leg is of length 'x', the hypotenuse will be 'x√2'.

Front

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

Back

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

Front

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

Back

To find the hypotenuse in a 45-45-90 triangle, multiply the length of one leg by √2.

Front

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

Back

To find the length of the longer leg in a 30-60-90 triangle, multiply the length of the shortest side (opposite the 30° angle) by √3.

Front

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

Back

The hypotenuse is 5√2.

Front

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the shorter leg?

Back

The shorter leg (opposite the 30° angle) is 5.

Front

What is the formula to calculate the area of a right triangle?

Back

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

Front

How can you use special right triangles to solve real-world problems?

Back

Special right triangles can simplify calculations in real-world problems involving heights, distances, and angles, allowing for quick and accurate solutions.

Front

What is the significance of the 30-60-90 triangle in trigonometry?

Back

The 30-60-90 triangle is significant in trigonometry because it provides specific sine, cosine, and tangent values for the angles 30°, 60°, and 90°.