Right triangle

Definition

A right triangle is a triangle in which one angle measures exactly 90 degrees. The side opposite this angle is called the hypotenuse, and the other two sides are known as the legs.

5 Must Know Facts For Your Next Test

1. The Pythagorean theorem applies to right triangles: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
2. In a right triangle, sine of an angle is defined as the ratio of the length of the opposite side to the hypotenuse: $\sin(\theta) = \frac{opposite}{hypotenuse}$.
3. Cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{adjacent}{hypotenuse}$.
4. Tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $\tan(\theta) = \frac{opposite}{adjacent}$.
5. The angles in a right triangle always add up to 180 degrees, with one angle being 90 degrees.

Review Questions

• What is the relationship between the sides of a right triangle according to the Pythagorean theorem?
• How do you define sine and cosine for angles in a right triangle?
• If one angle in a right triangle is 90 degrees, what must be true about the sum of all angles in that triangle?

Related terms

Hypotenuse: The longest side of a right triangle, opposite the right angle.

$\sin(\theta)$: The sine function which gives the ratio of the length of the opposite side to the hypotenuse in a right triangle.

$\cos(\theta)$: The cosine function which gives the ratio of length of adjacent side to hypotenuse in a right triangle.