Solving a Triangle (SAS): Another Example (8.1.3)

Question 1

• Review: The law of sines: (sin a)/a = (sin b)/b = (sin y)/c.

Answer 1

• Review: The law of sines: (sin a)/a = (sin b)/b = (sin y)/c.

Question 2

• If the side opposite the given angle is shorter than the adjacent side, there may be two triangles. If so, solve for both sets of possibilities. The possibilities are:
• The opposite side is shorter than the altitude. If so, no triangle exists.
• The opposite side is longer than the altitude and shorter than the adjacent side. If so, two triangles may be possible.
• The opposite side is longer than the adjacent side. If so, one triangle is possible.

Answer 2

• If the side opposite the given angle is shorter than the adjacent side, there may be two triangles. If so, solve for both sets of possibilities. The possibilities are:
• The opposite side is shorter than the altitude. If so, no triangle exists.
• The opposite side is longer than the altitude and shorter than the adjacent side. If so, two triangles may be possible.
• The opposite side is longer than the adjacent side. If so, one triangle is possible.