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Cogito

Trigonometry · Chapter 7 · Lesson 3

Practice Worksheet

Area of Any Triangle

When you cannot see the height.

12 problems · about 21 minutes · G-SRT.D.9, G-SRT.D.11

NameDate

Figure — use these to answer the problems

Check the formula on a right triangle: with C = 90°, sin C is 1 and ½ab is the ordinary area.
adjacent = 6opposite = 4hyp = 7.2133.69°
  • sin — opposite over hypotenuse0.55
  • cos — adjacent over hypotenuse0.83
  • tan — opposite over adjacent0.67
  • The marked angle33.69°
Adjacent leg6
Opposite leg4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Sides 10 and 4, included angle 30°. What is the area?

    Answer

  2. The angle in ½ab sin C must be which one?

    • The angle between the two sides.
    • The largest angle in the triangle.

  3. Sides 8 and 10, included angle 30°. Area?

    Answer

  4. Sides 6 and 6, included angle 90°. Area?

    Answer

  5. Sides 3, 4, 5 with s = 6. What is the Heron area?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Sides 5, 5, 6. What is s?

    Answer

  2. Sides 5, 5, 6 with s = 8. What is the area?

    Answer

  3. Sides 20 and 14, included angle 90°. Area?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each situation by which formula fits.

    Write each item under the heading it belongs to: Two sides and the angle between them · All three sides, no angles · Sides 7 and 9 with a 40° angle between · Sides 6, 7 and 8

    Use ½ab sin C

    Use Heron

  2. Sides 12 and 5, included angle 90°. Area?

    Answer

  3. The Garden

    Sides 10 and 12 with an included angle of 30°. What is the area?

    Answer

  4. The Three Sides

    A triangle has sides 3, 4 and 5. What is s in Heron’s formula?

    Answer