7. Non-Right Triangles

Law of Cosines

Textbook Question
CONCEPT PREVIEW Assume a triangle ABC has standard labeling.

a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.

b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.

a, B, and C
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Textbook Question
Find the exact area of each triangle using the formula 𝓐 = ½ bh, and then verify that Heron's formula gives the same result.

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Textbook Question
Find the area of each triangle ABC.

a = 76.3 ft, b = 109 ft, c = 98.8 ft
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Textbook Question
Find the length of the remaining side of each triangle. Do not use a calculator.

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Textbook Question
In Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle.A = 162°, b = 11.2, c = 48.2
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Textbook Question
In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 5, b = 7, C = 42°
675
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Textbook Question
In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.b = 5, c = 3, A = 102°
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Textbook Question
In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 6, c = 5, B = 50°
686
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Textbook Question
Use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)
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Textbook Question
In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit.a = 2 meters, b = 4 meters, c = 5 meters
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Textbook Question
In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 5, c = 2, B = 90°
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Textbook Question
In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit.a = 2 meters, b = 2 meters, c = 2 meters
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Textbook Question
Use one or more of the six sum and difference identities to solve Exercises 13–54. In Exercises 13–24, find the exact value of each expression. cos(135° + 30°)
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Textbook Question
In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 5, b = 7, c = 10
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Textbook Question
In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 3, b = 9, c = 8
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