B Apply

17. Think About a Plan One of the congruent sides of an isosceles triangle is 10 cm long. One of the congruent angles has a measure of 54 ° . 54 degrees . Find the perimeter of the triangle. Round your answer to the nearest centimeter.
    • Can drawing a diagram help you solve this problem?
    • What information do you need before finding the perimeter?
    • How can you find that information?

18. Forestry A forest ranger in an observation tower sights a fire 39 ° 39 degrees east of north. A ranger in a tower 10 miles due east of the first tower sights the fire at 42 ° 42 degrees west of north. How far is the fire from each tower?

    
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19. Geometry The sides of a triangle are 15 in., 17 in., and 16 in. The smallest angle has a measure of 54 ° . 54 degrees . Find the measure of the largest angle. Round to the nearest degree.

Find the remaining sides and angles of Δ DEF . cap delta Round your answers to the nearest tenth.

20. m ∠ D = 54 ° , m ∠ E = 54 ° , m angle d equals , 54 degrees comma , m angle e equals , 54 degrees comma and d = 20 d equals 20
21. m ∠ D = 54 ° , e = 8 m angle d equals , 54 degrees comma , e equals 8 m, and d = 10 d equals 10
22. Reasoning In Δ ABC , a = 10 cap delta and b = b equals 15.
    1. Does the triangle have a greater area when m ∠ C = 1 ° m angle c equals , 1 degrees or when m ∠ C = 50 ° ? m angle c equals , 50 degrees question mark
    2. Does the triangle have a greater area when m ∠ C = 50 ° m angle c equals , 50 degrees or when m ∠ C = 179 ° ? m angle c equals , 179 degrees question mark
    3. For what measure of ∠ C angle c does Δ ABC cap delta have the greatest area? Explain.
23. Open-Ended Sketch a triangle. Specify three of its measures then use the Law of Sines to find the remaining measures.

Find the area of Δ ABC . cap delta Round your answer to the nearest tenth.

24. m ∠ C = 68 ° , b = 12.9 m angle c equals , 68 degrees comma , b equals , 12.9 , c = 15.2 c equals , 15.2
25. m ∠ A = 52 ° , a = 9.71 m angle eh equals , 52 degrees comma , eh equals , 9.71 , c = 9.33 c equals , 9.33
26. m ∠ A = 23 ° , m ∠ C = 39 ° , b = 14.6 m angle eh equals , 23 degrees comma , m angle c equals , 39 degrees comma , b equals , 14.6
27. m ∠ B = 87 ° , a = 10.1 m angle b equals , 87 degrees comma , eh equals , 10.1 , c = 9.8 c equals 9.8

In Δ ABC , m ∠ A = cap delta 40° and m ∠ B = m angle b equals 30°. Find each value to the nearest tenth.

28. Find AC for B C = 10.5 b c equals , 10.5 m.
29. Find BC for A C = 21.8 eh c equals , 21.8 ft.
30. Find AC for A B = 81.2 eh b equals , 81.2 yd.
31. Find BC for A B = 5.9 eh b equals 5.9 cm.
32. Measurement A vacant lot is in the shape of an isosceles triangle. It is between two streets that intersect at an 85 . 9 ° 85 . 9 degrees angle. Each of the sides of the lot that face these streets is 150 ft long. Find the perimeter of the lot to the nearest foot.
33. 1. In the diagram below, m ∠ A = 30 ° , A B = 10 , m angle eh equals , 30 degrees comma eh b equals 10 comma and B C = b c equals BD = 6 . equals 6 . Use the Law of Sines to find m ∠ m angle D, m ∠ angle ABD, and m ∠ m angle ABC.

    2. Reasoning Notice that two sides and a nonincluded angle of Δ ABC cap delta are congruent to the corresponding parts of Δ ABD , cap delta but the triangles are not congruent. Must Δ EFG cap delta be congruent to Δ ABD cap delta if E F = 10 , F G = 6 , e f equals 10 comma f g equals 6 comma and ∠ E ≅ ∠ A angle , e approximately equal to , angle eh ? Explain.

    
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