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Cogito

Integrated Math 2 · Chapter 5 · Lesson 2

Practice Worksheet

Solving Right Triangles

Finding a missing side or angle.

12 problems · about 21 minutes · G-SRT.C.8

NameDate

Figure — use these to answer the problems

Set the legs and read the angle. Solving a triangle is doing that computation by hand.
adjacent = 5opposite = 5hyp = 7.0745°
  • sin — opposite over hypotenuse0.71
  • cos — adjacent over hypotenuse0.71
  • tan — opposite over adjacent1
  • The marked angle45°
Adjacent leg5
Opposite leg5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Legs 6 and 8. What is the hypotenuse?

    Answer

  2. Two sides are known and you want the angle. What do you use?

    • An inverse trigonometric function.
    • The ordinary ratio.

  3. Legs 7 and 24. Hypotenuse?

    Answer

  4. Legs 8 and 15. Hypotenuse?

    Answer

  5. tan θ = 1. What is θ, in degrees?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. sin θ = 0.5. What is θ, in degrees?

    Answer

  2. Which ratio holds opposite and adjacent? 1 sine, 2 cosine, 3 tangent.

    Answer

  3. Hypotenuse 20, opposite 10. Sine as a decimal?

    Answer

Stretch Yourself

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

4 problems

  1. Put the solving process in order.

    Write 1 to 4 in the boxes to put these in order.

    • Mark the angle you are working from.
    • Label the sides opposite, adjacent and hypotenuse.
    • Choose the ratio holding what you know and want.
    • Substitute and solve, then check the answer is sensible.

  2. Legs 20 and 21. Hypotenuse?

    Answer

  3. The Ladder

    A right triangle has legs 9 and 12. What is the hypotenuse?

    Answer

  4. The Equal Legs

    A right triangle has equal legs. What is each acute angle, in degrees?

    Answerdegrees