5-3 Unit 5 Trigonometry.

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Presentation transcript:

5-3 Unit 5 Trigonometry

Solve the system of equations Do Now 5-3 Solve the system of equations Essential Question: What is the hypotenuse of a 45-45-90 triangle with a leg length of 5√3?

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

Good Things!

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

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

Notes: Special Right Triangles Some right triangles have special relationships There are only TWO “special right triangles” 45-45-90 Triangles 30-60-90 Triangles

Notes: 45-45-90 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?

Notes: 45-45-90 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?

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

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

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

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

Special Right Triangles Angle Measures 45° 45° 90° 30° 60° 90° Side Lengths a a a√2 a a√3 2a

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

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

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

Exit Ticket