Pythagorean Theorem, Special Right Triangles and Trig Ratios

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). It can be expressed as: a² + b² = c².

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What are special right triangles?

Back

Special right triangles are triangles with specific angle measures that allow for easy calculation of side lengths. The two most common special right triangles are the 45-45-90 triangle and the 30-60-90 triangle.

Front

What is the side length ratio in a 45-45-90 triangle?

Back

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

Front

What is the side length ratio in 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 1 is the length of the side opposite the 30-degree angle, √3 is the length of the side opposite the 60-degree angle, and 2 is the length of the hypotenuse.

Front

How do you find the length of a side in a right triangle using the Pythagorean Theorem?

Back

To find the length of a side in a right triangle, rearrange the Pythagorean Theorem formula (a² + b² = c²) to solve for the unknown side. For example, if you know the lengths of the other two sides, you can calculate the hypotenuse as c = √(a² + b²).

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is the definition of a hypotenuse?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is the relationship between the sides of a right triangle?

Back

The relationship between the sides of a right triangle is defined by the Pythagorean Theorem, which states that the sum of the squares of the two shorter sides equals the square of the hypotenuse.

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How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if they satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Front

What is a trigonometric ratio?

Back

A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).