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Cogito

Trigonometry · Chapter 1 · Lesson 3

Practice Worksheet

Special Right Triangles

Two triangles worth knowing by heart.

12 problems · about 20 minutes · G-SRT.C.8

NameDate

Figure — use these to answer the problems

Set both legs equal for a 45-45-90 triangle, then check the angle really is 45°.
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. In a 30-60-90 triangle, the hypotenuse is 20. What is the short leg?

    Answer

  2. Which triangle comes from cutting a square in half?

    • The 45-45-90 triangle.
    • The 30-60-90 triangle.

  3. sin 30° as a decimal?

    Answer

  4. cos 60° as a decimal?

    Answer

  5. tan 45° as a decimal?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A 30-60-90 triangle has short leg 5. What is the hypotenuse?

    Answer

  2. A 45-45-90 triangle has legs 7. Hypotenuse to two decimal places?

    Answer

  3. sin 60° to three decimal places?

    Answer

Stretch Yourself

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

4 problems

  1. Match each angle with its sine.

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

    • 30°
    • 45°
    • 60°
    • 1/2
    • √2/2
    • √3/2

  2. A 30-60-90 triangle has short leg 4. Long leg to two decimal places?

    Answer

  3. The Square

    A square has sides of 10. What is the diagonal, to two decimal places?

    Answer

  4. The Ramp

    A 30-60-90 triangle has hypotenuse 12. What is the short leg?

    Answer