13. In Δ DEF , d = 15  in  . , e = 18 cap delta in., and f = 10 f equals 10 in. Find m ∠ F . m angle f .
14. In Δ ABC , a = 20 m , b = 14 cap delta m, and c = 16 c equals 16 m. Find m ∠ A . m angle eh .
15. In Δ DEF , d = 12  ft  , e = 10 cap delta ft, and f = 9 ft. f equals 9 ft. Find m ∠ F . m angle f .

Use the Law of Cosines and the Law of Sines. Find x to the nearest tenth. See Problem 3.

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18. In Δ ABC , b = 4  in  . , c = 6 cap delta in., and m ∠ A = 69 ° . m angle eh equals , 69 degrees . Find m ∠ C . m angle c .
19. In Δ RST , r = 17  cm  , s = 12 cap delta cm, and m ∠ T = 13 ° . m angle t equals , 13 degrees . Find m ∠ S . m angle s .
20. In Δ DEF , d = 20  ft  , e = 25 cap delta ft, and m ∠ F = 98 ° . m angle f equals , 98 degrees . Find m ∠ D . m angle d .

B Apply

For each triangle, write the correct form of the Law of Cosines or the Law of Sines to solve for the measure in red. Use only the information given in blue.

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27. Think About a Plan A touring boat was heading toward an island 80 nautical miles due south of where it left port. After traveling 15 nautical miles, it headed 8 ° 8 degrees east of south to avoid a fleet of commercial fishermen. After traveling 6 nautical miles, it turned to head directly toward the island. How far was the boat from the island at the time it turned?
    • Can a diagram help you understand the problem?
    • What are you asked to find?
    • Which measurements do you need to solve the problem?
28. Sports A softball diamond is a square that is 65 ft on a side. The pitcher's mound is 46 ft from home plate. How far is the pitcher from third base?

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