Question

Use the Law of Sines to solve the triangle. Round your answers to two decimal places.

Answer 1

Answer: 37.1

Explanation: The Law of sines states that there is a proportionality between a side of triangle and its correspondent angle, i.e.:

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

where:

a, b and c are sides

A, B and C are angles

In the question, there is a triangle with 27.4 as a measure of side a, angles A and C. So, it wants the side c:

$\frac{a}{sinA} = \frac{c}{sinC}$

$\frac{27.4}{sin(99.7)} = \frac{c}{sin(20.4)}$

c = $\frac{27.4.sin(20.4)}{sin(99.7)}$

c = 37.1

The side c is 37.1