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G-SRT.11 Warmup M3-043-A02-V04

Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.

Report every complete SSA triangle solution

Problem

For the SSA triangle shown, \(A~=~35°\), \(a~=~9\), and \(b~=~14\). Find every valid triangle, including \(B\), \(C\), \(c\), and the total number of solutions.

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Keep only principal B≈63.2°, giving C≈81.8° and c≈15.5, and report 1 triangle without testing the supplement.

Use both correct angle pairs but match b=14 with A=35° when finding c, giving c≈23.1 and c≈6.5 instead of the corresponding values.

sin(B)=14sin(35°)/9≈0.892. The valid solutions are B≈63.2°, C≈81.8°, c≈15.5 and B≈116.8°, C≈28.2°, c≈7.4, so 2 triangles exist.

Reverse the ratio to get sin(B)=9sin(35°)/14≈0.369; accept B≈21.7° and 158.3°, including C≈-13.3°, and report 2 triangles.

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Curriculum context

Course: Math III
Standard: G-SRT.11
Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Objective: Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.
Problem type: Report every complete SSA triangle solution