SL Math

Sin and Cosine Rule

Hey guys!

     Exciting news!! We have FINALLY reached Chapter 10 in our SL Mathematics book, which means we are almost halfway done with our curriculum. Currently, we are learning about triangular trigonometry. It's not the easiest math in the world, but it's definitely a step up from the circular trigonometry we were doing last month! In this lesson, we learned all about the sin and cosine rules that you could use for finding the side length or angle of a triangle. (P.S.) In the examples below, the lines to show a fraction do not show up on our web page. However, it is fairly obvious to realize where the factions are so it shouldn't be too confusing!

     The following information was found on this website: http://www.cimt.plymouth.ac.uk/projects/mepres/step-up/sect4/index.htm

Formula for right-angled triangles:

Formula for all triangles:

(Ignore the yellow highlight)

Here's how you would go about finding side "x" in the diagram below:

Step 1:	Start by writing out the Sine Rule formula for finding sides:       a = b sin(A) sin(B)
Step 2:	Fill in the values you know, and the unknown length:       x = 7 sin(80°) sin(60°)
Step 3:	Solve the resulting equation to find the unknown side, giving your answer to 3 significant figures: x = 7      (multiply by sin(80°) on both sides) sin(80°) sin(60°) x = 7 × sin(80°) sin(60°) x = 7.96 (accurate to 3 significant figures)

 Here's how you would go about finding angle "m" in the diagram below:

Step 1:	Start by writing out the Sine Rule formula for finding angles:       sin(A) = sin(B) a b
Step 2:	Fill in the values you know, and the unknown angle:       sin(m°) = sin(75°) 8 10
Step 3:	Solve the resulting equation to find the sine of the unknown angle: sin(m°) = sin(75°)      (multiply by 8 on both sides) 8 10 sin(m°) = sin(75°) × 8 10 sin(m°) = 0.773 (3 significant figures)
Step 4:	Use the inverse-sine function (sin–1) to find the angle: m° = sin–1(0.773) = 50.6° (3sf) - Sophie F.