Week 11, Lesson 1 1. Warm Up 2. Notes Sine, Cosine, Tangent 3. ICA Triangles
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1 Week 11, Lesson 1 1. Warm Up 2. Notes Sine, Cosine, Tangent 3. ICA Triangles HOW CAN WE FIND THE SIDE LENGTHS OF RIGHT TRIANGLES? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question 55 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Find the area of the following triangles: 16cm 9in 10in 6mm 32cm 14in 9mm 1
2 Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Side Lengths of Right Triangles Pythagorean Theorem: c b Can be used to find the missing side of a right triangle Must be given 2 side lengths c is always the hypotenuse a Eample 1: Find the missing sides of the following triangles
3 Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Side Lengths of Right Triangles Sine Cosine Tangent: adjacent opposite opposite OR hypotenuse hypotenuse These are proportions that work every time θ stands for the angle θ is a variable, just like You must be given 1 side length AND 1 angle adjacent Eample 2: triangles Find the missing sides of the following 5 c y b 13 Summary: In your own words, write out an eplanation of the Pythagoran Theorem and Sine, Cosine, Tangent so that an 8th grader who has never seen this would understand it 3
4 Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 11, Lesson 2 1. Warm up 2. Notes Inverse Trig. Functions 3. ICA Super Triangle HOW DO YOU SOLVE FOR THE ANGLES OF A TRIANGLE? 57 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Without using the Pythagorean Theorem, solve for the missing sides of the triangle. 18cm : y: y 4
5 Opposite Week 11 Sin, Cos, Tan.notebook Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Inverse Trig Functions Missing Angles: Use inverse trig functions Sin 1 Cos 1 Tan 1 Opposite Hypotenuse Hypotenuse Adjacent Adjacent Eample 1 Complete the triangle 20in 13in Eample 2 Complete the triangle 21in 15in Eample 3 Find θ 40.2cm 12cm Summary: 5
6 ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Triangles Complete the Triangle 16in z a b 10in c y m n d 6
7 Week 11, Lesson 3 1. Warm up 2. Notes Law of Sin Law of Cos 3. ICA Practice Problems HOW CAN SIN AND COS WORK FOR NON RIGHT TRIANGLES? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question 59 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Complete the triangle using any method. 7cm y 22cm z = y= z= 7
8 Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Law of Sines Corresponding Sides & Angles: Law of Sines: An angle's corresponding side is on the OPPOSITE side of the triangle A c b B The ratios of any side length to the sin of its corresponding angle are proportionate a C Given A corresponding pair and any other part Use this to find a missing side OR angle Eample 1: Complete the following triangle 12cm 15cm Summary: = 8
9 Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Law of Cos Law of Cosine: Given in order A side, an angle, a side Answer the missing side length Given All 3 sides Answer The angle Eample 2 Complete the triangle below 10in 12in Eample 3 Complete the triangle below using Law of Cosine, then Law of Sine 5cm 10cm 12cm Summary: 9
10 e ity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Test Like Question 10
11 Week 11, Lesson 4 1. Warm up 2. ICA Completing an Object 3. QUIZ Trig. WHAT IS THE ESSENTIAL QUESTION? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question 61 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Complete the following triangle z 110in y 11
12 ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Complete the following objects 12cm 18cm z b y a = y= z= c a= b= 22in m r y 12in s n 16in 12
13 Attachments W2L1.doc Project Survey.doc Project Survey.ls Project Questionnaire.doc Project Questionnaire.ls
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