Cogito
Trigonometry · Chapter 7 · Lesson 1
The Law of Sines and Cosines
Triangles without a right angle.
10 problems · about 21 minutes · G-SRT.D.10, G-SRT.D.11
What this lesson teaches
The student applies the Law of Sines and the Law of Cosines to solve non-right triangles.
- The Law of Sines needs a matched side and opposite angle.
- The Law of Cosines handles three sides, or two sides and the included angle.
- Pythagoras is the Law of Cosines with a right angle.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Modelling with Sinusoids: Max 30, min 10. What is the amplitude?
Answer 10
Why 10.
Review — Half Angle Formulas: cos A = 0.6. What is sin²(A/2)?
Answer 0.2
Why 0.2.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSides 9 and 12 with a 90° angle between them. Third side?
Answer 15
Why 15.
Why is Pythagoras a special case of the Law of Cosines?
Answer cos 90° is 0, so the last term vanishes.
Why The correction term disappears at 90°.
Sides 5 and 12 with a 90° angle between. Third side?
Answer 13
Why 25 + 144.
What is cos 90°?
Answer 0
Why x-coordinate at the top.
Build It Up
The same ideas with more to keep track of.
2 problemsThree sides known, no angles. Which law?
Answer The Law of Cosines.
Why Sines needs a matched pair.
A side and its opposite angle known, plus another angle. Which law?
Answer The Law of Sines.
Why You have a matched pair.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Right Angle: In the Law of Cosines, what is cos 90°?
Answer 0
Why 0, which is why Pythagoras is a special case.
The Special Case: Sides 6 and 8 with a 90° angle between them. What is the third side?
Answer 10
Why 10.