Leg

Definition

In the context of geometry, a leg refers to one of the sides of a triangle or right-angled figure. Legs are the perpendicular sides that form the right angle, and they are essential in understanding properties of angles, triangles, and the Pythagorean Theorem.

5 Must Know Facts For Your Next Test

1. The lengths of the legs in a right triangle are used to calculate the length of the hypotenuse using the Pythagorean Theorem.
2. The sum of the angles in a triangle is always 180 degrees, and the angles formed by the legs of a right triangle are always 90 degrees.
3. The ratio of the lengths of the legs in a right triangle determines the trigonometric functions, such as sine, cosine, and tangent.
4. The legs of a triangle can be used to classify the type of triangle, such as isosceles (two equal legs) or scalene (no equal legs).
5. The lengths of the legs in a right triangle can be used to find the area of the triangle using the formula: Area = (1/2) × base × height.

Review Questions

• Explain how the lengths of the legs in a right triangle are used to calculate the length of the hypotenuse using the Pythagorean Theorem.
  • The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides, the legs. Specifically, the formula is: $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse. By knowing the lengths of the legs, you can use this formula to solve for the length of the hypotenuse.
• Describe how the angles formed by the legs of a right triangle are related to the sum of the angles in a triangle.
  • In a right triangle, the angles formed by the legs are always 90 degrees. This is because the sum of the angles in a triangle is always 180 degrees, and in a right triangle, one of the angles is a 90-degree right angle. The other two angles must then add up to 90 degrees. This relationship between the angles in a right triangle is an important property that is used in various geometric proofs and applications.
• Analyze how the ratio of the lengths of the legs in a right triangle can be used to determine the trigonometric functions.
  • The trigonometric functions, such as sine, cosine, and tangent, are defined in terms of the ratios of the lengths of the sides of a right triangle. Specifically, the sine of an angle is the ratio of the length of the opposite leg to the length of the hypotenuse, the cosine is the ratio of the length of the adjacent leg to the length of the hypotenuse, and the tangent is the ratio of the length of the opposite leg to the length of the adjacent leg. By knowing the lengths of the legs in a right triangle, you can use these definitions to calculate the trigonometric functions, which are essential in many applications of geometry and physics.

Related terms

Hypotenuse:

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

Acute Angle:

An angle that measures less than 90 degrees.

Obtuse Angle:

An angle that measures more than 90 degrees.