7. Non-Right Triangles

Law of Sines

Open Question
A painter is going to apply paint to a triangular metal plate on a new building. Two sides measure 16.1 m and 15.2 m, and the angle between the sides is 125°. What is the area of the surface to be painted?
Open Question
A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are 52.1 m and 21.3 m, and the angle between them is 42.2°. What is the area of the triangular lot?
Open Question
Use the law of sines to find the indicated part of each triangle ABC.

Find A if C = 79° 20', c = 97.4 mm, a = 75.3 mm
Open Question
Determine the number of triangles ABC possible with the given parts.

a = 31, b = 26, B = 48°
Open Question
Determine the number of triangles ABC possible with the given parts.

c = 50, b = 61, C = 58°
Open Question
In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.A = 56°, C = 24°, a = 22
Open 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.B = 37°, a = 12.4, b = 8.7
Open Question
In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.A = 85°, B = 35°, c = 30
Open Question
In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.B = 5°, C = 125°, b = 200
Open Question
In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.B = 80°, C = 10°, a = 8
Open Question
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.a = 30, b = 20, A = 50°
Open Question
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.a = 57.5, c = 49.8, A = 136°
Open Question
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.a = 6.1, b = 4, A = 162°
Open Question
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.a = 10, b = 30, A = 150°
Open Question
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.a = 30, b = 40, A = 20°