Special Right Triangles, Pythagorean Theorem, Radicals

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios, such as the 45-45-90 triangle and the 30-60-90 triangle.

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Front

What are the side ratios 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, where the shortest side is opposite the 30° angle.

Front

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

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

What is a radical in mathematics?

Back

A radical is a symbol that represents the root of a number, most commonly the square root, denoted by √.

Front

How do you simplify √(a²)?

Back

√(a²) simplifies to |a|, which is the absolute value of a.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is d = √((x₂ - x₁)² + (y₂ - y₁)²), which calculates the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.