1. SEE SOMETHING, SAY SOMETHING
ACT RESPONSIBLY & SUPPORT the COMMUNITY.
Be on Time
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SEE SOMETHING, SAY SOMETHING

2. Learning Objective
We will determine1 how to use the Special Right Triangle to determine and find the side lengths.
What are we going to do?
What is determine means?_______.
CFU
Activate Prior Knowledge
The Greek letter theta ( ) is used to represent the measure of an angle in a right triangle.
Opposite(Opp) – Is a position on the other side of a specific angle from; facing.
Hypotenuse
Opposite
Adjacent(Adj) -next to something else.
Hypotenuse(Hyp )- the longest side of a right triangle, opposite the right angle (90 ). o
Adjacent
Use a Trigonometric Ratio to find the value of x.
Students, you already know identify the sides in a right triangle. Today, we will learn how to use the Special Right Triangle to determine and find the side lengths..
Make Connection
Hypotenuse
1 Figure out
Vocabulary
Opposite
x = 37

3. Concept Development
A trigonometric ratio is a ratio of two sides of a right triangle. You have already seen SOH-CAH-TOA, which represents all three ratios.
Recall: The point (x, y). The x will now be represented by Cos and y will be represented by Sin.
On your whiteboard, Identify the following using the Unit Circle:
cos 30° =
2. sin 30° =
3. cos 45° =
4. sin 45° =
5. cos 60° =
6. sin 60° =
CFU
(0, 1)
(1, 0)
(-1, 0)
(0, -1)

4. Find the given side lengths and angle measurements for triangle ABC.
Concept Development
On your whiteboard, Find the indicated values from the figure.
RT =
RS =
Sin 30° =
Tan 60° =
CFU
In geometry, an isosceles triangle is a triangle that has two sides of equal length. 
Pythagorean Theorem
Find the given side lengths
and angle measurements
for triangle ABC.

5. Hawk Dance of Miwok Indians
Concept Development
The Miwok Indian Tribe that at one time lived in the area which we now know as Delhi used the word
Hawk Dance
of Miwok Indians
to help them remember the trigonometric ratios.

6. Skill Development/Guided Practice
Trigonometric ratios are formed by comparing the lengths of two sides of a right triangle from the “viewpoint” of a given acute angle.
Steps to find Trig Ratio 1 2 3 4
How did I/you know which angle to use?
How did I/you identify the Opposite, Adjacent, & Hypotenuse sides?
How did I/you find the unknown side length?
CFU 1 2 3
Identify the angle to “look” through.
Identify the Opp , Adj , and Hyp side to the angle.
Remember the Concept
Write down the Ratio.
SOH-CAH-TOA
Solve for the Unknown.
1. For the triangle, find the unknown side
lengths and trigonometric ratios for the 45°
angles.
2. Find the unknown side lengths in each
right triangle.

7. The tree is about 76 feet tall. Write the ratio Substitute values
Relevance Reason #1: Trig Ratio are used in finding the height.
You are measuring the height of a Sitka spruce tree in Alaska. You stand 45 feet from the base of the tree. You measure the angle of elevation from a point on the ground to the top of the top of the tree to be 59°. To estimate the height of the tree, you can write a trigonometric ratio that involves the height h and the known length of 45 feet.
tan 59° =
opposite
adjacent
Write the ratio
tan 59° = h 45
The tree is about
76 feet tall.
Check for Understanding
Does anyone else have another reason why it is relevant to use verb tense correctly?
Which reason is most relevant to you? Why?
Substitute values
45 tan 59° = h
Multiply each side by 45
45 (1.6643) ≈ h
Sample Item
75.9 ≈ h
Simplify
Find Sin, Cos, Tan of T. Leave answer as a fraction.
Relevance Reason #2: Know how to find Trig Ratios will help you do well on tests: (PSAT, SAT, ACT, GRE, GMAT, LSAT, etc..).

8. What did you learn today about how to use the Special Right Triangle to determine and find the side lengths.
Word Bank
Unit Circle
Triangle
Triangle .
SUMMARY CLOSURE
Today, I learned how to __________________
______________________________________________________________.