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Cogito

Geometry · Chapter 5 · Lesson 1

Practice Worksheet

The Three Ratios

Similarity is why they work at all.

10 problems · about 21 minutes · G-SRT.C.6, G-SRT.C.7, G-SRT.C.8

NameDate

Figure — use these to answer the problems

The three ratios are computed from the triangle you build.
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 Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “The Side-Splitter Theorem”

    Third side 16. Midsegment?

    Answer

  2. From “Similar Figures and Scale”

    Sides in ratio 4. Area ratio?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Legs 5 and 12. Hypotenuse?

    Answer

  2. Why does the sine of an angle not depend on the triangle size?

    • All such triangles are similar, so the ratios match.
    • Because that is the definition.

  3. Legs 6 and 8. Hypotenuse?

    Answer

  4. Opposite 3, hypotenuse 5. Sine, as a decimal?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

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

    Answer

  2. Does scaling a triangle change its sine?

    • No.
    • Yes.

Stretch Yourself

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

2 problems

  1. The Ratio

    A right triangle has legs 3 and 4. What is the hypotenuse?

    Answer

  2. The Tangent

    Opposite 6, adjacent 8. What is the tangent, as a decimal?

    Answer