Find b, given that angle A= 50°, angle C=55°, a=30. (Round to the nearest hundredth.)

Since we are given angles and sides, we can solve for what we are looking for by using the Law of Sines. Since we are looking for side b, and we are given both side a and angle A, the Law of Sines for us looks like this:

[tex]\frac{sinB}{b}=\frac{sinA}{a}[/tex]

Since b is our unknown, we need angle B in order to use the Law of Sines. We know A and C, so we can find B by using the Triangle Angle-Sum Theorem:

180 - 50 - 55 = 75

Angle B = 75. Therefore,

[tex]\frac{sin75}{b}=\frac{sin50}{30}[/tex]

Cross multiply to solve for b:

30sin50 = bsin50 and

[tex]b=\frac{30sin75}{sin50}[/tex]

b = 37.83

raphealnwobi raphealnwobi · Answer 2 · 2022-04-29T12:38:39+02:00

The measure of side b in triangle ABC with ∠A= 50°, ∠C=55°, a=30 is b = 37.83

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

50 + ∠B + 55 = 180

∠B = 75°

Using sine rule:

b/sinB = a/sinA

b/sin(75) = 30 / sin(50)

b = 37.83

The measure of side b in triangle ABC with ∠A= 50°, ∠C=55°, a=30 is b = 37.83

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