Geometry Formulas

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: $$a^2 + b^2 = c^2$$ .

The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.

The area (A) of a triangle can be calculated using the formula: $$A = \frac{1}{2}bh$$ , where b is the base and h is the height.

The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

To find the length of a side using the cosine function, you can use the formula: $$\cos(\theta) = \frac{adjacent}{hypotenuse}$$ .

For complementary angles, the sine of one angle is equal to the cosine of the other: $$\sin(\theta) = \cos(90° - \theta)$$ .

The area (A) of a rectangle can be calculated using the formula: $$A = l \times w$$ , where l is the length and w is the width.

The circumference (C) of a circle can be calculated using the formula: $$C = 2\pi r$$ , where r is the radius.

The volume (V) of a rectangular prism can be calculated using the formula: $$V = l \times w \times h$$ , where l is the length, w is the width, and h is the height.