Pythagorean Theorem and Special Right Triangles

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.

Front

What are the special right triangles?

Back

The special right triangles are the 45-45-90 triangle and the 30-60-90 triangle. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is √2 times the length of a leg. In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

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 c is the hypotenuse and a and b are the lengths of the other two sides.

Front

What is the sine function in relation to a right triangle?

Back

The sine function (sin) of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. It can be expressed as: sinA = opposite/hypotenuse.

Front

What is the cosine function in relation to a right triangle?

Back

The cosine function (cos) of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. It can be expressed as: cosA = adjacent/hypotenuse.

Front

What is the tangent function in relation to a right triangle?

Back

The tangent function (tan) of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. It can be expressed as: tanA = opposite/adjacent.

Front

In a 30-60-90 triangle, what is the relationship between the sides?

Back

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

Front

In a 45-45-90 triangle, what is the relationship between the sides?

Back

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

Front

How do you calculate the sine of an angle given the lengths of the sides?

Back

To calculate the sine of an angle, divide the length of the opposite side by the length of the hypotenuse: sinA = opposite/hypotenuse.

Front

What is the opposite side in relation to an angle in a right triangle?

Back

The opposite side is the side that is directly across from the angle in question.