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Cogito

Trigonometry · Chapter 7 · Lesson 1

Practice Worksheet

The Law of Sines and Cosines

Triangles without a right angle.

10 problems · about 21 minutes · G-SRT.D.10, G-SRT.D.11

NameDate

Figure — use these to answer the problems

The right-angle case is where the Law of Cosines loses its last term.
adjacent = 3opposite = 4hyp = 553.13°
  • sin — opposite over hypotenuse0.80
  • cos — adjacent over hypotenuse0.60
  • tan — opposite over adjacent1.33
  • The marked angle53.13°
One side3
Other side4
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Modelling with Sinusoids”

    Max 30, min 10. What is the amplitude?

    Answer

  2. From “Half Angle Formulas”

    cos A = 0.6. What is sin²(A/2)?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Sides 9 and 12 with a 90° angle between them. Third side?

    Answer

  2. Why is Pythagoras a special case of the Law of Cosines?

    • cos 90° is 0, so the last term vanishes.
    • It is a coincidence.

  3. Sides 5 and 12 with a 90° angle between. Third side?

    Answer

  4. What is cos 90°?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Three sides known, no angles. Which law?

    • The Law of Cosines.
    • The Law of Sines.

  2. A side and its opposite angle known, plus another angle. Which law?

    • The Law of Sines.
    • The Law of Cosines.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Right Angle

    In the Law of Cosines, what is cos 90°?

    Answer

  2. The Special Case

    Sides 6 and 8 with a 90° angle between them. What is the third side?

    Answer