Question

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

A = 99.7°, C = 20.4º, a = 27.4​

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.:

`(a)/(sinA) = (b)/(sinB) = (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:

`(a)/(sinA) = (c)/(sinC)`

`(27.4)/(sin(99.7)) = (c)/(sin(20.4))`

c =
`(27.4.sin(20.4))/(sin(99.7))`

c = 37.1

The side c is 37.1