Back to Apply Law of Sines and Cosines — Problem 3 · Task Set 24

Exercises: Apply the Law of Sines and the Law of Cosines

Grade 10·22 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-srt-d-11

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Fluency Practice

In triangle $ABC$ , angle $A = 30\degree$ , side $a = 8$ , and side $b = 12$ . Compute $\sin B = \dfrac{b \sin A}{a} = \dfrac{12 \times 0.5}{8} = 0.75$ . How many valid triangles exist with these measurements?

No valid triangles — $\sin B > 1$

Exactly one triangle — the acute triangle only

Exactly two triangles — $B \approx 48.6\degree$ or $B \approx 131.4\degree$

Exactly one triangle — the obtuse triangle only