7. Non-Right Triangles

Law of Sines

Open Question
In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit.A = 22°, b = 20 feet, c = 50 feet
Open Question
In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit.B = 125°, a = 8 yards, c = 5 yards
Open Question
In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit.C = 102°, a = 16 meters, b = 20 meters
Open Question
In Exercises 43–44, use the given measurements to solve the following triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.a = 400, b = 300
Open Question
In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
a. two triangles
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Open Question
In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
b. exactly one triangle
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Open Question
In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
c. no triangle
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Open Question
Without using the law of sines, explain why no triangle ABC can exist that satisfies A = 103° 20', a = 14.6 ft, b = 20.4 ft.
Open Question
Apply the law of sines to the following:

A = 104°, a = 26.8, b = 31.3.

What happens when we try to find the measure of angle B using a calculator?
Open Question
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)
Open Question
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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Open Question
Use the law of sines to find the indicated part of each triangle ABC.

Find A if B = 39° 50', b = 268 m, a = 340 m