Physics for Technology, Second Edition, 2nd Edition

Appendix A

Trigonometry Review

Trigonometry shows us the relationship between the sides of a triangle and its angles. It is very useful in solving vector problems in two or three dimensions.

A.1   PYTHAGOREAN THEOREM AND RIGHT TRIANGLES

A right triangle is a triangle with a 90° angle.

Key points about a right triangle:

• ■ The hypotenuse long side of the triangle.

• ■ α +θ = 90 °

• ■ Pythagorean theorem: The hypotenuse equals the square root of the sum of the squares of the sides.

$$\begin{array}{l}C=\sqrt{A^2+B^2}\\ A=\sqrt{C^2-B^2}\\ B=\sqrt{C^2-A^2}\end{array}$$

FIGURE A.1   A right triangle has one 90 degree angle.

Example A.1

Find the length of the sides of the following right triangles: (a) A =3, ...