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Determine the area of a triangle given side-angle-side information.

Objectives. Determine the area of a triangle given side-angle-side information. Use the Law of Sines to find the side lengths and angle measures of a triangle.

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Determine the area of a triangle given side-angle-side information.

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  1. Objectives Determine the area of a triangle given side-angle-side information. Use the Law of Sines to find the side lengths and angle measures of a triangle.

  2. When you use the Law of Sines to solve a triangle for which you know side-side-angle (SSA) information, zero, one, or two triangles may be possible. For this reason, SSA is called the ambiguous case.

  3. Solving a Triangle Given a, b, and mA

  4. Remember! When one angle in a triangle is obtuse, the measures of the other two angles must be acute.

  5. C b a A B c Example 3: Art Application Determine the number of triangular banners that can be formed using the measurements a = 50, b = 20, and mA = 28°. Then solve the triangles. Round to the nearest tenth. Step 1 Determine the number of possible triangles. In this case, A is acute. Because b < a; only one triangle is possible.

  6. Example 3 Continued Step 2 Determine mB. Law of Sines Substitute. Solve for sin B.

  7. m B = Sin-1 Example 3 Continued Let B represent the acute angle with a sine of 0.188. Use the inverse sine function on your calculator to determine mB. Step 3 Find the other unknown measures of the triangle. Solve for mC. 28° + 10.8° + mC = 180° mC = 141.2°

  8. Example 3 Continued Solve for c. Law of Sines Substitute. Solve for c. c ≈ 66.8

  9. Check It Out! Example 3 Determine the number of triangles Maggie can form using the measurements a = 10 cm, b = 6 cm, and mA =105°. Then solve the triangles. Round to the nearest tenth. Step 1 Determine the number of possible triangles. In this case, A is obtuse. Because b < a; only one triangle is possible.

  10. Check It Out! Example 3 Continued Step 2 Determine mB. Law of Sines Substitute. Solve for sin B. sin B ≈ 0.58

  11. m B = Sin-1 Check It Out! Example 3 Continued Let B represent the acute angle with a sine of 0.58. Use the inverse sine function on your calculator to determine m B. Step 3 Find the other unknown measures of the triangle. Solve for mC. 105° + 35.4° + mC = 180° mC = 39.6°

  12. Check It Out! Example 3 Continued Solve for c. Law of Sines Substitute. Solve for c. c ≈ 6.6 cm

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