Question

The following figure shows ABC with side links to the nearest 10th find m

Answer 1

We have to find the measure of angle at vertex B.

We can use the Law of sines, that let us write proportions between the sine of an angle of the triangle and the sides.

This law tells us that the quotient between the sine of an angle of the triangle and the length of the opposite side is equal for each of the three angles of the triangle.

So in this case we can write:

`(\sin(C))/(AB)=(\sin (B))/(AC)`

We can replace the values we already know and calculate the measure of B as:

`\begin{gathered} \sin (B)=(AC)/(AB)\cdot\sin (C) \\ \sin (B)=(10)/(14)\cdot\sin (59\degree) \\ \sin (B)\approx(10)/(14)\cdot0.857 \\ \sin (B)\approx0.612 \\ B\approx\arcsin (0.612) \\ B\approx37.75\degree \end{gathered}`

Answer: B = 37.75°