## Description

Directions: Solve each of the following problems

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## Explanation & Answer

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The sine theorem:

𝑎

𝑏

𝑐

=

=

.

sin 𝐴 sin 𝐵 sin 𝐶

In this context, angles are denoted with capital letters (the angle vertex),

while sides — with small letters (side 𝑎 is opposite to the angle 𝐴).

1. 𝐴 = 77°, 𝐶 = 23°, 𝑐 = 16, find 𝑎.

𝑎

𝑐

sin 𝐴

sin 77°

= sin 𝐶, i.e. 𝑎 = 𝑐 ∙ sin 𝐶 = 16 ∙ sin 23° ≈ 𝟑𝟗. 𝟗.

sin 𝐴

2. 𝑞 = 25, 𝑃 = 13°, 𝑄 = 70°, find 𝑝.

𝑝

𝑞

sin 𝑃

sin 13°

= sin 𝑄, i.e. 𝑝 = 𝑞 ∙ sin 𝑄 = 25 ∙ sin 70° ≈ 𝟔. 𝟎.

sin 𝑃

3. 𝑦 = 18, 𝑌 = 39°, 𝑍 = 51°, find 𝑧.

𝑦

sin 𝑌

𝑧

sin 𝑍

sin 51°

= sin 𝑍, i.e. 𝑧 = 𝑦 ∙ sin 𝑌 = 18 ∙ sin 39° ≈ 𝟐𝟐. 𝟐.

4. 𝑏 = 27, 𝐴 = 82°, 𝐵 = 58°, find 𝑎.

𝑎

sin 𝐴

𝑏

sin 𝐴

sin 82°

= sin 𝐵, i.e. 𝑎 = 𝑏 ∙ sin 𝐵 = 27 ∙ sin 58° ≈ 𝟑𝟏. 𝟓.

5. 𝑡 = 9, 𝑇 = 29°, 𝑃 = 110°, find 𝑝.

𝑝

sin 𝑃

𝑡

sin 𝑃

= sin 𝑇, i.e. 𝑝 = 𝑡 ∙ sin 𝑇 = 9 ∙

sin 110°

sin 29°

≈ 𝟏𝟕. 𝟒.

6. 𝑒 = 22, 𝐸 = 81°, 𝐺 = 26°, find 𝑔.

𝑒

sin 𝐸

𝑔

sin 𝐺

sin 26°

= sin 𝐺 , i.e. 𝑔 = 𝑒 ∙ sin 𝐸 = 22 ∙ sin 81° ≈ 𝟗. 𝟖.

The sine theorem:...