Section 9-1

This week in Advanced Math we started on Chapter 9. In section 9-1, we learned how to find the unknown sides to a right triangle. We already learned this in geometry but now we are taking a few extra steps to solve these problems. The key to this section is to remember SOHCAHTOA. It stands for:

Sine = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

The reciprocals for these formulas are:

Cosecant = Hypotenuse/Opposite
Secant = Hypotenuse/Adjacent
Cotangent = Adjacent/Opposite

*Hypotenuse is always going to be opposite of the right angle.

Let’s try an example problem:

EXAMPLE 1:

Solve triangle ABC
Angle A = 90° Angle B = 36° a = 28

1) Since we already know angles A & B we must find C. You will subtract angles 90° and 36°from 180° to get an answer of 54°.
2) To get sides b and c you will need to use angle B. To solve for side b,
you will use sine's opposite/hypotenuse. Sin 36° = b/28
3) Multiply to get 28 Sin 36° = 16. 458
4) To get side c you will use cosine’s opposite/adjacent. Cos 36° = c/28
5) Multiply to get 28 Cos 36° = 22.652

Angle A = 90°
Angle B = 36°
Angle C = 54°
Side a = 28
Side b = 16.458
Side c = 22.652