7. Non-Right Triangles

Use the law of sines to prove that each statement is true for any triangle ABC, with corresponding sides a, b, and c.

(a - b)/(a + b) = (sin A - sin B)/(sin A + sin B)

A balloonist is directly above a straight road 1.5 mi long that joins two villages. She finds that the town closer to her is at an angle of depression of 35°, and the farther town is at an angle of depression of 31°. How high above the ground is the balloon? 

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In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.

In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.

In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.

In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.

In Exercises 41–42, find a to the nearest tenth.

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In Exercises 45–46, find the area of the triangle with the given vertices. Round to the nearest square unit. (-2, -3), (-2, 2), (2, 1)

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 = 107°, C = 30°, c = 126

In oblique triangle ABC, A = 34°, B = 68°, and a = 4.8. Find b to the nearest tenth.

In Exercises 39–40, find h to the nearest tenth.

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Fill in the blank(s) to correctly complete each sentence.

A triangle that is not a right triangle is a(n) _________ triangle.

Consider each case and determine whether there is sufficient information to solve the triangle using the law of sines.

Three sides are known.

A ship is sailing due north. At a certain point the bearing of a lighthouse 12.5 km away is N 38.8° E. Later on, the captain notices that the bearing of the lighthouse has become S 44.2° E. How far did the ship travel between the two observations of the lighthouse?