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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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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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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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.

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?

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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