math

Pythagorean Theorem

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides: $a^2 + b^2 = c^2$.

Right Triangle

A triangle with one angle measuring 90 degrees.

Special Right Triangles

Triangles with angles measuring 30-60-90 and 45-45-90, which have specific ratio properties.

Trigonometric Ratios

Ratios that relate the angles of a triangle to the lengths of its sides, including sine, cosine, and tangent.

Law of Sine

A ratio that relates the lengths of the sides of a triangle to the sine of its angles: $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$.

Law of Cosine

A rule stating that in any triangle, $c^2 = a^2 + b^2 - 2ab\cos(C)$, which relates the lengths of the sides to the cosine of one angle.

Angle of Elevation

The angle formed by the line of sight and the horizontal line when looking up at an object.

Angle of Depression

The angle formed by the line of sight and the horizontal line when looking down at an object.

Word Problems Involving Right Triangles

Real-world problems that can be solved using the properties of right triangles and trigonometric ratios.