Law of Sine and Cosine

This week in advanced math we started chapter 9, we learned law of sine and law of cosine. You may consider the law of cosine easier simply because after you have plugged all angles and sides into the formula you just plug that same formula into your calculator to get your answer. You must examine your problem very closely in order to know which law to use, be sure that all requirements of a formula are there in your triangle. It is hard to learn what formulas to use with which triangles. Along with law of sine and law of cosine there is SOHCAHTOA which involves a right triangle.

Law of Sines is used with a non-right triangle and an angle and opposite leg value that you know.
Formula: sin(angle) / opp leg = sin(angle 2) / opp leg 2
**cross multiply to solve

Ex 1: In triangleABC, angleS=126°, s= 12 and t=7 Determine whether angleT exists.
1.First draw and label the triangle.
2.Now we take our formula and plug our values into it.

Sin126°/12 = sinT/7 (multiply by 7 on each side)
7sin126°/12 =sinT
T= sinINVERSE(7sin126°/12)
T=28.159°

Law of Cosines is used when there is no pair in a non-right triangle.
Formula: (oppleg)^2 = (adjleg)^2 + (adjleg^2) – 2(adj leg) (adj leg) cos (angle between)

Ex 1: Suppose 2 sides of a triangle have lengths of 10cm and 8 cm and the angle between them measures to be 140 degrees. Find the 3rd side.

Once you draw your triangle, you plug the numbers into the formula.

X^2 = 10^2 + 8^2 – 2 (8)(10)cos140
Now we must square root the and the right side as well to get x.
Once that is done you can plug it into your calculator, make sure when you plug this into your calculator you put parenthesis.

And TADAAAAA X= 16.928