## Description

Directions: Solve each of the following problems.

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## Explanation & Answer

The solutions are written and checked. I answered "how many triangles" for each question. I am ready to find the remaining angles and sides if you need them.

𝑐

2

1. From the sine theorem, sin 𝐶 = 𝑎 sin 𝐴 = 3 sin 34° ≈ 0.37.

There are two possible angles with this sine, about 22° and about 180° − 22° = 158°.

The second angle is impossible because 34° + 158° > 180°, so the answer is 1.

𝑏

15

2. From the sine theorem, sin 𝐵 = 𝑎 sin 𝐴 = 19 sin 50° ≈ 0.60.

There are two possible angles with this sine, about 37° and about 180° − 37° = 143°.

The second angle is impossible because 50° + 143° > 180°, so the answer is 1.

𝑐

5

3. From the sine theorem, sin 𝐶 = 𝑎 sin 𝐴 = 7 sin 60° ≈ 0.62.

There are two possible angles with this sine, about 38° and about 180° − 38° = 142�...