Question

What is the measure of angle A? O 19.47 degrees O 18.43 degrees O 0.33 degrees O 70.53 degrees

Answer 1

To solve we use the law of sines, of which we have the following equation:

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

We have the triangle shown below.

As you can see, we start by assuming a right angle at the face angle to the 12' segment.

In this case, the values of the equation for the triangle are as follows

`\begin{gathered} a=4 \\ b=12 \\ \sin (A)=\sin (A) \\ \sin (B)=\sin (90)=1 \end{gathered}`

Now, we replace the values and solve for "A"

`\begin{gathered} (4)/(\sin(A))=(12)/(\sin(90)) \\ \sin (A)=(4)/(12)\cdot\sin (90) \\ A=\sin ^(-1)((4)/(12)\cdot1) \\ A=19.47122\cong19.47 \end{gathered}`

In conclusion, the answer is approximately 19.47 degrees