How do I solve this?

Question

The problem is: "Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A = 80° 20',  C = 53.7°,  c = 17.9"

I understand the whole Law of Sines thing and how to use it, and I Googled what the apostrophe is (it signifies angular minutes, right?) but I'm stuck because I don't know how to solve a problem like that with angular minutes. Before today, I'd never even heard of angular minutes.

Answer 1

Hi Anya, it is very similar to the (good old!) analog clock- remember the minute hand and the second hand?

A circle has 360°;

each degree is divided into 60 minutes and

each minute is sub divided into 60 seconds.

For example, 70°50' is read as 70 degrees and 50 minutes which is equivalent to the mixed fraction

70 5/6 degree or 70.8333°

Again another example- 15° 12" is equivalent to 15.0033°

Answer 2

usually they use the same letter for the angle and for the opposite side

so C = 53.7 degrees is opposite side c = 17.6 inches (" for inches)

A= 80 degrees 20' means 80 20/60 degrees = 80 1/3 degrees, sin801/3 = .985

sinA/a = sinC/c = .806/17.6 = .0458 = .985/a

a =.985/.0458 = 21.502 inches

B = 180- 80 1/3 - 53.7 = 45.967 = 45 degrees 58 minutes

sinB = .719

b/.719 = 17.6/.806

b = 15.699 inches

C= 53.7 degrees = 53 degrees 42 minutes

It's almost a 17.6 x 16 x 21.5 triangle with angles 46,80, and 54 degrees

sin80/21.5 = sin54/17.6 = sin46/16 =about 0.045 or 0.046. longest side is opposite the largest angle. smallest side opposite the smallest angle. Middle side opposite the middle angle.