Answer:
The length of a is equal to 14.9.
The angle measure of b is equal to 71°.
The length of c is equal to 25.5.
General Formulas and Concepts:
Pre-Calculus
Law of Sines:
[tex]\displaystyle \bold{ \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} }[/tex]
Step-by-step explanation:
Step 1: Define
Identify given from triangle.
Length corresponding with x°: 14.9
Other given angle: 71°
Length corresponding with 71°: 25.5
Step 2: Find Values
- [Law of Sines] Substitute in variables:
[tex]\displaystyle \frac{\sin x^\circ}{14.9} = \frac{\sin 71^\circ}{25.5}[/tex] - Isolate x° term:
[tex]\displaystyle \sin x^\circ = \frac{14.9 \sin 71^\circ}{25.5}[/tex] - Isolate x°:
[tex]\displaystyle x^\circ = \sin^{-1} \bigg( \frac{14.9 \sin 71^\circ}{25.5} \bigg)[/tex] - Identify variables:
[tex]\displaystyle a = 14.9 , \ b = 71^\circ , \ c = 25.5[/tex]
∴ we have completed the expression using Law of Sines.
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Topic: Precalculus
Unit: Trigonometry
