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Geometry/Trig Lesson 13-9: Final Exam Review 9 [Unit 11: Non-Right Triangle Trigonometry] Name: ______________________________ Date: _______________________________ Learning Goals Achieved in this Unit 1. How do we use the Law of Sines to solve for missing sides/angles in a non-right triangle? 2. How do we use the Law of Cosines to solve for missing sides/angles in a non-right triangle? 3. How can I apply Law of Sines and Law of Cosines to real-world applications of non-right triangle trigonometry? When to use each Law: ο· When given two sides and two angles use the _______________________________, including what we are finding! ο· When given three sides and one angle use the ________________________________ including what we are finding! Law of Cosines (to find a side): 2 2 Law of Sines: π = πππ(π΄) Law of Cosines (to find an angle): The angle we are looking for must always correspond with a 2 The side you are looking for must always be __________________________ with the angle used ο· a is always the side we are looking for Donβt forget to ___________________________ your final answer πΆππ (π΄) = ο· ο· ο· ο· πππ(π΅) *Corresponding means __________________________ or across from* π = π + π β 2ππ β πΆππ (π΄) ο· π (π 2 +π 2 βπ2 ) (2ππ) A is always the angle we are looking for DO NOT forget to USE PARANTHESIS around the numerator AND denominator Inverse Cosine your answer to find an _____________ Other Things to Remember: When finding an angle you must use ___________________________________________ ο· Lower case letters represent ___________________ of a triangle. The sides and are always opposite their corresponding angle. ο· Included angle: Angle in between the two given sides. ο· First always determine which law to use before setting up your equation! ο· Sometimes you need to find an angle before you begin using one of the laws ο· Donβt forget to round and label your units! Geometry/Trig Letβs Analyze a Student Sample and Correct the Work! As you look over this sample, make corrections in a different color! STUDENT SAMPLE Notes A playground is being built in the shape of the triangle ABC below. Find the length of the missing side AB of the playground rounded to the nearest hundredth. What did the student do well? Our Corrections What mistake(s) did the student make? Letβs Try One Together! A cross country race is taking place, and Matt is trying to figure out the distance of the course. He receives a map of the course, which is in the shape of a triangle. However, the map he receives was misprinted. He only has 5 minutes until the race starts, and he wants to know how far he will have to run in order to complete the course. a. Find the missing side of the triangular trail that was misprinted to the nearest meter. Geometry/Trig b. Calculate the total distance Matt with run during his race. Your Turn! 1. In triangle DEF, d = 65, f = 40, and mβ πΈ = 22°. Which equation can be used to determine the value of e? (Hint: Draw a picture first) a. 652 = 402 + π 2 β 2(65)(π)cos(22°) b. π 2 = 402 + 652 β 2(40)(65)cos(22°) c. πΆππ (22°) = 402 +652 βπ 2 (40)(65) d. 402 = 652 + π 2 β 2(40)(π)cos(22°) 2. Given the following triangle, what property/law would I use to solve for the missing side x? a. Law of Cosines b. SOH CAH TOA c. Law of Sines d. Pythagorean Theorem 3. In the accompanying diagram of Ξπ΄π΅πΆ, πβ π΄ = 80°, πβ π΅ = 43° and side BC = 25. What is the length of side AB to the nearest tenth? a. b. c. 10.1 36.1 17.3 Geometry/Trig d. 18.5 4. Find the smallest angle to the nearest tenth of a degree of a triangle whose sides are 8, 12,19. a. Which law will we use here? b. Find the measurement of the smallest angle to the nearest tenth of a degree. 5. A playground is being built in the shape of the triangle ABC below. Using either law, find the length of the missing side BC of the playground rounded to the nearest whole number. Geometry/Trig 6. The diagram below shows displays triangle ABC. a) Find the missing side to the nearest tenth. b) Find the perimeter of triangle ABC. 7. a. What is the measure ofβ‘π? b. Find the missing side of the following triangle. Round your answer to the nearest hundredth. Geometry/Trig 8. Given triangle QRS, mβ‘π = 71°, π πππ ππ = 400ππ‘, πππ π πππ ππ = 570ππ‘. Find the measurement of β‘π to the nearest degree.