Warm up: Solve for θ

θ

11

7

Welcome to the wonderful world of TRIANGLES!

WARNING:• Today’s material ONLY applies to Right

Triangles. • Soon we will be working with non-right

triangles, and will not be able to use these rules.

LABELS• When we label triangles, we typically use CAPITAL

letters for the Angles, and lower case letters for the sides.

• The letter on the side should correspond to the opposite angle.

• The side opposite the right angle is always the hypotenuse.

• Given an angle θ, the side touching it is called the “adjacent” side, and the side opposite it is the “opposite” side.

• Sine, Cosine and Tangent are all trigonometric functions. They come from the “Unit Circle”. You will learn more about them as functions in Pre-Calc.

• We will not go into depth about the functions themselves, instead we will use our handy dandy calculators!

Sin, Cos, Tan

Now we are ready for Soh Cah Toa

• We use Soa Cah Toa to find missing angles AND missing side lengths of right triangles.

• To find a missing angle, you need at least 2 side lengths.

• To find a missing side length, you need either the other two side lengths, or one side length and one angle (2 things total).

Soh Cah Toa

Cos

Tan

Example 1:

θ

35

30

Solve for θ.

Well, first we need to figure out what position each number is in relation to the angle we want to find:30 = opposite side35= hypotenuse.

Then we ask, of Soh Cah Toa, which uses opp and hyp? Sin! Then we simply plug the numbers in and solve.

.85714…..

Example 1 Cont…Uh Oh! One more step.

.85714…..But we don’t want the Sin of θ, we want θ.

Now we need our calculators. To get θ by itself, we will use “Sin Inverse”, which looks like .(.85714…) = 58.98°, and so θ = 58.98°.

Check your calculator!

• Didn’t get that answer?

• Make sure your calculator is in the “degree” mode.

• Go to mode, and if it is in “radians” switch it to degrees.

Now you Try!

Find θ:

θ

37

12

Solution:

• Tan• Tan• Tan• θ• θ=72.03°

θ

37

12

72.03°

37

12

You Try Again!• Find the Sin,

Cos and Tan Ratios for θ.

• Note: Do not actually solve for θ.

θ

55

3270

Solution

Cos

Tan

θ

55

3270

Homework

• Page 489• Problems: 1, 4, 5,