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Cogito

Geometry · Chapter 5 · Lesson 2

Practice Worksheet

Solving Right Triangles

Choosing the ratio that has what you know.

11 problems · about 24 minutes · G-SRT.C.8

NameDate

Figure — use these to answer the problems

Change the legs and watch the ratios and the angle follow.
adjacent = 4opposite = 3hyp = 536.87°
  • sin — opposite over hypotenuse0.60
  • cos — adjacent over hypotenuse0.80
  • tan — opposite over adjacent0.75
  • The marked angle36.87°
Adjacent leg4
Opposite leg3
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Legs 7 and 24. Hypotenuse?

    Answer

  2. Legs 3 and 4. Hypotenuse?

    Answer

  3. Legs 5 and 12. Hypotenuse?

    Answer

  4. Hypotenuse 13, one leg 5. Other leg?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Match each pair of known parts to the ratio you would use.

    Draw a line from each item on the left to its match on the right.

    • Opposite and hypotenuse
    • Adjacent and hypotenuse
    • Opposite and adjacent
    • Sine
    • Cosine
    • Tangent

  2. Legs 9 and 12. Hypotenuse?

    Answer

  3. Can a leg be longer than the hypotenuse? 1 for yes, 0 for no.

    Answer

Stretch Yourself

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

4 problems

  1. Legs 8 and 15. Hypotenuse?

    Answer

  2. Two sides known, third wanted, no angles. Use Pythagoras? 1 for yes, 0 for no.

    Answer

  3. The Third Side

    Legs 6 and 8. What is the hypotenuse?

    Answer

  4. The Longest Side

    Which side is always longest in a right triangle? 1 for a leg, 2 for the hypotenuse.

    Answer