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Cogito

Geometry · Chapter 5 · Lesson 3

Practice Worksheet

Special Right Triangles

Two triangles worth knowing by heart.

11 problems · about 22 minutes · G-SRT.C.6

NameDate

Figure — use these to answer the problems

Set both legs equal to see the 45-45-90 case.
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.

4 problems

  1. 30-60-90 with hypotenuse 18. Shortest side?

    Answer

  2. 30-60-90 with hypotenuse 20. Shortest side?

    Answer

  3. 30-60-90 with shortest side 7. Hypotenuse?

    Answer

  4. 45-45-90 with legs 6. What is the hypotenuse squared?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. In a 45-45-90, are the two legs equal? 1 for yes, 0 for no.

    Answer

  2. Match each triangle to its side ratio.

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

    • 45-45-90
    • 30-60-90
    • 1 : 1 : √2
    • 1 : √3 : 2

  3. Which angle faces the shortest side in a 30-60-90? Give the degrees.

    Answer

Stretch Yourself

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

4 problems

  1. A 45-45-90 is half of which shape? 1 for square, 2 for equilateral triangle.

    Answer

  2. 30-60-90 with hypotenuse 30. Shortest side?

    Answer

  3. Half the Hypotenuse

    A 30-60-90 with hypotenuse 12. What is the shortest side?

    Answer

  4. The Square

    A 45-45-90 with legs 1. What is the hypotenuse squared?

    Answer