7. Non-Right Triangles

Law of Cosines

Open 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
Open Question
A plane has an airspeed of 520 mph. The pilot wishes to fly on a bearing of 310°. A wind of 37 mph is blowing from a bearing of 212°. In what direction should the pilot fly, and what will be her ground speed?
Open Question
Find the force required to keep a 75-lb sled from sliding down an incline that makes an angle of 27° with the horizontal. (Assume there is no friction.)
Open Question
A crane with a counterweight is shown in the figure. Find the horizontal distance between points A and B to the nearest foot.

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Open Question
A boat travels 15 km per hr in still water. The boat is traveling across a large river, on a bearing of 130°. The current in the river, coming from the west, has a speed of 7 km per hr. Find the resulting speed of the boat and its resulting direction of travel.
Open 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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Open Question
Find the area of each triangle ABC.

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

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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.A = 162°, b = 11.2, c = 48.2
Open 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°
Open 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°
Open 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°
Open Question
In Exercises 14–19, use a sum or difference formula to find the exact value of each expression.cos(45° + 30°)
Open 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
Open 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°