find af and mf.....

Question

Given: △AMF, m∠A=28° m∠F=49°, AM = 12 Find: AF, MF

Answer: AF≈ units, MF≈ units

Answer 1

For this question, we would need to use our law of sines with our triangle points:

SinA / a = SinM / m = SinF / f.

Before doing this, however, we should find our missing angle M. We know that there are a total of 180 degrees in a triangle, so we just have to subtract the other two angles from 180. 180 - 49 - 28 = 103. So angle M must be 103 degrees.

Now we can plug in the information we have into the law of sines:

Angle A = 28 degrees

Angle F = 49 degrees

Angle M = 103 degrees

Side f (or AM as it is the side opposite angle F) = 12 units

Side a correlates to MF and Side m correlates to AF

Sin(28) / a = Sin(103) / m = Sin (49) / 12

Lets find side m first:

Sin(103) / m = Sin(49) / 12 - multiply both sides by m

Sin(103) = Sin(49) / 12 * m - multiply both sides by 12

12Sin(103) = mSin(49) - divide both sides by Sin(49)

12Sin(103) / Sin(49) = m - solve

m or AF should be about 15.5 units.

Side MF is the same as side a in the law of sines formula. So we can find it like this:

First, we set up our equation: Sin(28) / a = Sin(49) / 12

Next, we multiply both sides by a: Sin(28) = Sin(49) / 12 * a

Next, we multiply both sides by 12: 12Sin(28) = aSin(49)

Next, we divide both sides by Sin(49): 12Sin(28)/Sin(49) = a

Finally, we solve: a = 7.46 or approximately 7.5.

So a or MF is about 7.5.

Let me know if you have any questions!