Question

Find the missing parts of the triangle.B = 11.7°b= 8.75a= 10.79If necessary round angles to the nearest tenth and side lengths to the nearest hundredth.Option 1: A=14.48°, C=153.82°, c=19.04Option 2: A=165.52°, C=2.78°, c=2.09Option 3: no such triangleOption 4: A1= 14.48°, C1= 153.82°, c1=19.04;A2=165.52°, C2=2.78°, c2=2.09

Answer 1

Let's use the law of sines in order to find the angle A:

`\begin{gathered} (a)/(sin(A))=(b)/(sin(B)) \\ so: \\ (10.79)/(sin(A))=(8.75)/(sin(11.7)) \end{gathered}`

Solve for A:

`\begin{gathered} A=sin^(-1)((10.79\cdot sin(11.7))/(8.75)) \\ A\approx14.48 \end{gathered}`

Now, we can find the angle C using the triangle sum theorem:

`\begin{gathered} A+B+C=180 \\ 14.48+11.7+C=180 \\ 26.18+C=180 \end{gathered}`

Solve for C:

`\begin{gathered} C=180-26.18 \\ C\approx153.82 \end{gathered}`

Finally, let's find c using the law of sines again:

`\begin{gathered} (b)/(sin(B))=(c)/(sin(C)) \\ so: \\ (8.75)/(sin(11.7))=(c)/(sin(153.82)) \end{gathered}`

Solve for c:

`\begin{gathered} c=(8.75\cdot sin(153.82))/(sin(11.7)) \\ c\approx19.04 \end{gathered}`

Answer:

A = 14.48

C = 153.82

c = 19.04