Special Right Triangles

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is opposite the 90° angle.

Front

How do you find the hypotenuse of a 45-45-90 triangle if the leg length is 4?

Back

Multiply the leg length by √2. So, 4√2.

Front

What is the formula for the area of a square?

Back

Area = side². If the diagonal is known, use the formula Area = (diagonal²)/2.

Front

If the height of an equilateral triangle is known, how can you find the side length?

Back

Use the formula: side = (height * 2) / √3.

Front

What is the formula to find the length of the long leg in a 30-60-90 triangle?

Back

Multiply the length of the short leg by √3.

Front

What is the area of a square with a diagonal of 26?

Back

Area = (26²)/2 = 338.

Front

What is the value of x in a right triangle if the other two sides are 3 and 4?

Back

Use the Pythagorean theorem: x = √(3² + 4²) = 5.

Front

What is the relationship between the angles in a triangle?

Back

The sum of the interior angles in any triangle is always 180°.

Front

How do you find the length of the hypotenuse in a right triangle?

Back

Use the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.