4.3 Ambiguous Case for Sine Rule

In triangle ABC, ∠A = 13°, a = 2 cm, and b = 6 cm, how many triangles are formed?

• 0

• 1

• 2

• Can't determine

For ∆ABC, how many possible triangles can be drawn: ∠A = 75°, a = 15 cm, b = 12 cm?

• 0

• 1

• 2

• Can't determine

Find the measure of ∠ADB. (Round to a whole answer.)

• 25°

• 10°

• 58°

• 122°

Tags

CCSS.HSG.CO.C.9

Find the length of AC. (Since no units are given in the diagram, state the answer as a whole number.)

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Find the measure of line segment AD. (Since no units are given, record your answer as just the number rounded to the nearest whole number.)

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which scenario is the Ambiguous case concerned with?

• SSS

• SAS

• SSA

• AAS

Given the following information, ∠A = 28°, a = 4.3 mm, b = 9.2 mm, how many possible triangles can be formed?

• 0

• 1

• 2

• Not enough information given

Given the following information, ∠B = 73°, a = 7 mm, b = 5 mm, how many possible triangles can be formed?

• 0

• 1

• 2

• Not enough information given.

Calculate the height of the triangle, to the nearest tenth of a centimetre. ∆RST, ∠R = 103°, r = 15 cm, and s = 8 cm.

• 14.6 cm

• 7.8 cm

• 4.2 cm

• 5.7 cm

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.9

Which set of measurements can produce two possible triangles?

• ∠A = 28°, a = 10.5 m, b = 15.0 m

• ∠A = 28°, a = 7.0 m, b = 15.0 m

• ∠A = 28°, a = 16.0 m, b = 15.0 m

• ∠A = 28°, a = 5.5 m, b = 15.0 m

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11