1. 5-3 Unit 5 Trigonometry

2. Solve the system of equations
Do Now 5-3
Solve the system of equations
Essential Question: What is the hypotenuse of a triangle with a leg length of 5√3?

3. Agenda Partner Practice Exit Ticket Do Now Good Things!!! Notes
Intro to Unit 5 – Trigonometry
Special Right Triangles
Partner Practice
Exit Ticket

4. Good Things!

5. Pythagorean Theorem Review
C is ALWAYS the hypotenuse!! If it doesn’t add up, it means you DON’T have a right triangle!

6. Pythagorean Theorem a.
Find the value of x. Express your answer in simplest radical form. b.
Is this a right triangle? Why or why not? 3 6 11 4 x 9

7. Notes: Special Right Triangles
Some right triangles have special relationships
There are only TWO “special right triangles”
Triangles
Triangles

8. Notes: Triangles
You know how to find any side length of a right triangle with the Pythagorean Theorem
1. We have a square with a side length of 2. What is the length of the diagonal?
2. We have a square with a side length of 6. What is the length of the diagonal? 2 6
If it’s a square, what will the new angle measures be?

9. Notes: Triangles
3. We have a square with a side length of 5. What is the length of the diagonal?
4. We have a square with a side length of 8. What is the length of the diagonal? 8 5
Notice a pattern?

10. Notes: 45-45-90 Triangles 7 Angle Measures 45° 90° Side Lengths a a√2
*draw in your notes
Angle Measures
45°
90°
Side Lengths a
a√2 7

11. Using the Pythagorean Theorem, find the length of the missing side.
Notes: Triangles
Using the Pythagorean Theorem, find the length of the missing side. 5.
90°
60°
30° 6.
90°
60°
30° 6 8 4 3

12. Using the Pythagorean Theorem, find the length of the missing side.
Notes: Triangles
Using the Pythagorean Theorem, find the length of the missing side. 7.
90°
60°
30° 8.
90°
60°
30° 10 14 7 5

13. Notes: 30-60-90 Triangles 30° 60° 90° a a√3 2a Angle Measures
*draw in your notes
Angle Measures
30°
60°
90°
Side Lengths a
a√3 2a

14. Special Right Triangles
Angle Measures
45° 45° 90°
30° 60° 90°
Side Lengths
a a a√2
a a√ a

15. Guided Practice 1 – Step by Step
Identify your angles
Identify your side lengths
-we are given a length x
-we are given a hypotenuse 8
Solve for a
8 = a√2
*isolate a*
8/√2 = a
*rationalize denominator*
8√2 / 2 = a
4√2 =a

16. Guided Practice 2 30 60 90
a a√ a
What type of special right triangle is this?
2a = 6
c. a = x; a√3 = y
d. Solve for a:
a = 3, so x = 3 and y = 3√3

17. Partner Practice
You have ~10 minutes to complete the 5 partner practice problems
We will review them together before you begin the exit ticket

18. Exit Ticket