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Cogito

Integrated Math 2 · Chapter 5 · Lesson 1

Practice Worksheet

The Three Trigonometric Ratios

Similarity gives every right triangle a fingerprint.

12 problems · about 21 minutes · G-SRT.C.6, G-SRT.C.7

NameDate

Figure — use these to answer the problems

Change the legs and watch all three ratios update together with the angle.
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.

5 problems

  1. Adjacent 12, hypotenuse 13. Cosine to two decimal places?

    Answer

  2. Why does one angle determine the ratios?

    • All right triangles with that angle are similar.
    • It is defined that way with no reason.

  3. Adjacent 4, hypotenuse 5. Cosine as a decimal?

    Answer

  4. Opposite 8, hypotenuse 10. Sine as a decimal?

    Answer

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

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Opposite 6, adjacent 8. Tangent as a decimal?

    Answer

  2. Can a sine ever exceed 1? 1 yes, 0 no.

    Answer

  3. Legs 5 and 12. What is the hypotenuse?

    Answer

Stretch Yourself

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

4 problems

  1. Match each ratio with its definition.

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

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

  2. Opposite 5, hypotenuse 13. Sine to two decimal places?

    Answer

  3. The Sine

    Opposite 3, hypotenuse 5. What is the sine, as a decimal?

    Answer

  4. The Tangent

    Opposite 3, adjacent 4. What is the tangent, as a decimal?

    Answer