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

What Is The Measure Of Angle A O 1947 Degrees O 1843 Degrees O 033 Degrees O 7053 Degrees class=

Sagot :

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

[tex]\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}[/tex]

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

[tex]\begin{gathered} a=4 \\ b=12 \\ \sin (A)=\sin (A) \\ \sin (B)=\sin (90)=1 \end{gathered}[/tex]

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

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

In conclusion, the answer is approximately 19.47 degrees

View image LujaneB139137