Unit 7 Solving Right triangles math 2.notebook April 17, 2018

Transcription

1 Warm Up Calculate the value of. Unit 7 Learning Intention: Given a right triangle, students will be able to write and use trigonometric ratios to solve right triangles. Success Criteria: 1. I will be able to identify the parts of right triangle. 2. I will be able to setup a proportion to find the missing sides of a right triangle. 3. I will be able to setup a proportion to find the missing angles of a right triangle. Mathematics enhances critical thinking and problem solving abilities. It provides perspective on real life events. Trigonometry is an area of mathematics that probes the property of triangles to help them solve problems. It is used in satellite systems and astronomy, aviation, engineering, land surveying, geography and many other fields. Real life pplication In fact, the depth of the value of triangle often etends to areas most people would never even dream of. For eample, did you know that triangles form the basis of a number of martial arts? k, that statement probably got your attention so let's eplain it. In the Indonesian martial art of Silat (Silat means fighting) the art is based around impacting an opponent of the weakness of the triangular base the body uses to stand. When you disrupt the triangle at a weak point, it becomes difficult to stand up! So, this is an entire martial art based around triangles and it is a lot easier on the body than breaking boards like in karate! Precisely, trigonometry is a branch of mathematics that deals with triangles, circles, waves and oscillations.

2 Vocabulary word definition drawing/eample Parts of a Right Triangle trigonometry study of angles and sides of triangles angle side opposite hypotenuse trigonometric ratios Reference angle a ratio of the lengths of 2 sides of a right triangle an acute angle of a right triangle sine cosine tangent adjacent 36 o reference angle leg opposite the leg across the reference angle leg adjacent the leg that does form the reference angle Trigonometric Ratios C B

3 Trigonometric Ratios shorter way to write them: sine > sin B = cosine > cos B = S C Find the following trig ratios: sin R = cos R = tan R = sin D = cos D = tan D = R 5 3 E D 4 tangent > tan B = remember S C T!!! T Now you try... Find the following trig ratios: sin L = cos L = tan L = S 12 Closure S 13 3 N 2 W Now you try... sin S = cos S = tan S = What do you notice about the sines and cosines you found? Do you think this relationship will be true for any pair of acute angles in a right triangle? Eplain. L 16 Find the following trig ratios: sin N = cos N = tan N =

4 Unit 7 Learning Intention: Given a right triangle, students will be able to write and use trigonometric ratios to solve right triangles. Success Criteria: 1. I will be able to identify the parts of right triangle. 2. I will be able to setup a proportion to find the missing sides of a right triangle. 3. I will be able to setup a proportion to find the missing angles of a right triangle. Trigonometric Ratios shorter way to write them: sine > sin B = cosine > cos B = tangent > tan B = remember S C T!!! S C T 1) Identify your reference angle. 2) Label the sides of the triangle. (opposite, hypotenuse, adjacent) Solve for. 8 3) Check which sides you know and use them to select your trig ratio. (S C T) 4) Write your trig equation Eplain to your partner how you set up the proportion to find the missing side. 20 o 5) Solve for the missing variable.

5 Solve for. 62 o 10 Solve for. 15 Eplain to your partner how you set up the proportion to find the missing side. Can you use either the sine or cosine ratio to find?eplain. 48 o Solve for. Solve for y o 8 53 o y Solve for. a) 21.2 b) 15.6 c) 13.2 d) 47.2 a) 10.0 b) 13.3 c) 6.0 d) 10.6

6 Find the missing side Warm up Unit 7 Learning Intention: Given a right triangle, students will be able to write and use trigonometric ratios to solve right triangles. Success Criteria: 1. I will be able to identify the parts of right triangle. 2. I will be able to setup a proportion to find the missing sides of a right triangle. 3. I will be able to setup a proportion to find the missing angles of a right triangle. So far we have used trigonometric ratios to find the missing side lengths of right triangles. Find the m<k K What if instead we would like to find the measure of an acute angle in a right triangle? Just like we found the missing sides of the right triangle, we can use trigonometric ratios to find the measure of an acute angle. By using the inverse trig functions: If sin =, then sin 1 = m < 8 L J 5 Find m <J using inverse cosine. Is the result what you epect? Eplain. If cos =, then cos 1 = m < If tan =, then tan 1 = m <

7 Find the m<r R Find the missing angle. Eplain. Warm up 12 S 35 T What other angle measures or lengths of Eplain how? RST can you find?