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Name:______________________________________________________ Date:__________________ Period:__________ Chapter 10: Applying Trig Functions Topic 1: Law of Cosines The law of cosines is a reference-sheet formula used to solve for missing sides or angles of a triangle. Similar to the _______________________________ ______________________. We use the law of cosines when we ______ __________ have a right triangle. The Law of Cosines is for Law of Cosines formulas Recall from Geometry: Sides are named by a lower-case letter which matches the angle is it __________________ ____________. Label the sides. Look for “book ends” Whether the unknown is a side or an angle, it must be either the beginning or end of the formula Follow the pattern to fill in the rest. Working with the formula & your calculator. First, always, draw & label a triangle. Take inventory of what you know and what you want to know (3 sides 1 angle: Law of Cosines) Rewrite the reference sheet formula specific to your question, starting with the bookends. Careful calculator work. Examples: 1. Find x to the nearest tenth: Name:______________________________________________________ Date:__________________ Period:__________ 2. Find e to the nearest tenth: 3. In , if 4. In , if , find z to the nearest unit. , find the measure of angle A to the nearest minute. Name:______________________________________________________ Date:__________________ Period:__________ Classwork 1. In triangle HAT, a = 6.4, t = 10.2, and m<H = 87. Find the length of side h to the nearest tenth. 2. The base angles of isosceles triangle GHI measure 54.7° while equal sides GH and HI measure 8.94 inches. Find the length of GI to the nearest hundredth. 3. In triangle ABC, side b = 12, side c = 20 and m<A = 45. Find side a to the nearest tenth. 4. Find the largest angle, to the nearest tenth of a degree, of a triangle whose sides are 9, 12, and 18. Name:______________________________________________________ Date:__________________ Period:__________ 5. A surveyor at point R sights two points S and T on opposite sides of a lake. Point R is 120m from S and 180m from T, and the measure of <R is 38o. Find the distance across the lake to the nearest meter. 6. In a rhombus with a side of 24, the longer diagonal is 36. Find, to the nearest tenth of a degree, the larger angle of the rhombus. 7. Three sides of a triangle measure 20, 30, and 40. Find the measure of the largest angle of a triangle to the nearest degree. 8. The Horticulture Club is designing a wildflower garden. They want to make it in the shape of a triangle whose sides have lengths 12 feet, 14 feet, and 18 feet. What is the measure of the smallest angle in the triangle to the nearest degree? Name:______________________________________________________ Date:__________________ Answer Key: 1.) 11.8 2.) 10.33 3.) 14.3 4.) 117.3 5.) 113 6.) 97.2 7.) 104 8.) 42 Period:__________