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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.
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