Length, Right Triangles Part 1

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: c² = a² + b².

Front

What are the properties of a right triangle?

Back

A right triangle has one angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are referred to as the legs.

Front

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

Back

To find the length of a side, rearrange the Pythagorean Theorem formula. For example, to find the length of side a, use: a = √(c² - b²).

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 angles and sides in a right triangle?

Back

In a right triangle, the side opposite the largest angle is the longest side (the hypotenuse), and the side opposite the smallest angle is the shortest side.

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height, where the base and height are the lengths of the two legs.

Front

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

Back

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. It can be expressed as: sin(θ) = opposite/hypotenuse.

Front

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

Back

In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. It can be expressed as: cos(θ) = adjacent/hypotenuse.

Front

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

Back

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. It can be expressed as: tan(θ) = opposite/adjacent.

Front

How do you find the length of the hypotenuse if the lengths of the legs are known?

Back

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