Question

PLEASE HELP ME!!!!!!!!!!!!!!In the triangle below, b=___. If necessary, round your answer to two decimal places.

Answer 1

40.1

Explanation:

Answer 2

First of all, we can find the angle B by using the fact that the interior angles of a triangle sum up to 180:

`32.5+26.8+B=180 \iff B = 180-32.5-26.8=120.7</p><p>`

Now use the law of sines, which states that the ratio between a side and the sine of its opposite angle is constant. In particular, we have

`\frac{\overwrite{BC}}{\sin(A)}=(b)/(\sin(B))`

Plug in the known values and solve for b:

`(25)/(\sin(32.5))=(b)/(\sin(120.7))\iff b=(25\sin(120.7))/(\sin(32.5))=40.01`