Geometry/Trig

Name: __________________________

Date: ______________________

Lesson 7-1: Intro to Trigonometric Functions Learning Goal: How can I set up ratios using right triangle trigonometry?

Warm-Up: a) Solve for the length of side BC? Leave your answer in simplest radical form.

b) In right triangle ABC, hypotenuse AB=15 and angle A=35º. Find leg length, BC, to the nearest tenth. Draw a picture!

How is the following question different from the one above? Why CAN’T we use Pythagorean Theorem here?

Side-Angle Relationships – Naming Triangles

Sometimes, we cannot use the Pythagorean Theorem, so we need to use ____________________________.

First, we need to know how to label and name sides of right triangles.

Angle-Side Relationships

Opposite Side

Adjacent Side

Hypotenuse

**How do we label sides of triangles?

Where is side ‘a’ located?

Sides of triangles are sometimes labeled by the angle _________________ them!

Using Angle B:

Opposite Side:

Adjacent Side:

Hypotenuse

Geometry/Trig

Let's Practice 1. What is the length of the side opposite from angle A? ________

2. What is the length of the side adjacent to angle B? _________

3. What is the length of the hypotenuse? __________

Trigonometric Ratios

*How can we remember this?

Often, mathematicians will use Greek letters to identify an angle in a right triangle.

“Theta” *Try writing some here:

Let’s try labeling the triangles below, using the angle indicated!

Watch me! You Try!

Geometry/Trig

Let's practice writing trig ratios!

1) The diagram below shows right triangle XYZ. Write the ratio that represents...

a) the sine of ∡X

b) the cosine of ∡X

c) the tangent of ∡ Y

d) the tangent of ∡X

You Try:

-Using triangle ABC, write the ratio that represents…

a) the sine of ∠A

b) the cosine of ∠C

c) the tangent of ∠C

d) the tangent of ∠A

Geometry/Trig

Practice:

1.

2.

What is the ratio that represents the Tan C? 3. Using the triangle to the right, write the ratio for Tan D:

Geometry/Trig

4. 5. 6.

Hint! Draw and

label the

triangle first!

Geometry/Trig

Think! 7. In the right triangle shown in the diagram below,

a) Label the sides of the triangle, according to the 30-degree angle (in terms of opposite, adjacent, and hypotenuse).

b) Which trig function do we have enough given information to use? (Use your answer from part a)

c) Write a trig ratio (sine, cosine, or tangent) using the 30-degree angle.