Question

Two sides and an angle SSA of a triangle are given determine whether the given measurements produce one triangle two triangles or no triangle at all solve each triangle that results a=13 b=16.9 A=26 degrees

Answer 1

Given:

a = 13

b = 16.9

A = 26 degrees

Asked: What are the values for angles B and C and side c?

Solution:

To solve this problem, we will be needing the formula for the sine law.

Sine Law Formula:

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

Now, we will first solve for the angle B.

`\begin{gathered} (a)/(\sin A)=(b)/(\sin B) \\ (13)/(\sin 26)=(16.9)/(\sin B) \\ 13\sin B=16.9\sin 26 \\ (13\sin B)/(13)=(16.9\sin 26)/(13) \\ \sin B=(16.9\sin26)/(13) \\ B=\sin ^(-1)((16.9\sin26)/(13)) \\ B=34.75203189 \\ B=35\text{ degr}ees \end{gathered}`

Now that we have angle B, we can now find angle C by combining all the angles and equate it to 180 degrees.

`\begin{gathered} A+B+C=180 \\ 26+35+C=180 \\ 61+C=180 \\ C=180-61 \\ C=119\text{ degr}ees \end{gathered}`

In order to find side c, we will use again the sine law formula.

`\begin{gathered} (a)/(\sin A)=(c)/(\sin C) \\ (13)/(\sin 26)=(c)/(\sin 119) \\ 13\sin 119=c\sin 26 \\ (13\sin119)/(\sin26)=(c\sin 26)/(\sin 26) \\ c=(13\sin119)/(\sin26) \\ c=25.9370542 \end{gathered}`

ANSWER:

Angle B = 35 degrees

Angle C = 119 degrees

Side c = 25.9