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All courses Math III · G-SRT.11 43 of 55
Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.

Solve both unknown sides in an AAS/ASA triangle

Problem
Which complete AAS/ASA solution is correct for a = 120 m, A = 35 degrees, and B = 72 degrees?
Prompt triangle with A=35°, B=72°, and side a=120 m; C and sides b and c are withheld. Open full size
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Hint

Compute the third angle and label which side is opposite each angle.

First use A+B+C=180, then write a/sin A=b/sin B=c/sin C with opposite pairs.

Solution walkthrough

01

Find third angle

\[C=180-35-72=73~\text{deg}\]

Triangle interior angles sum to 180 degrees.

02

Match opposite pairs

\[120/\sin35=b/\sin72=c/\sin73\]

Each numerator side must be opposite its denominator angle.

03

Solve first side

\[b=198.9739...~m~->~199.0~m\]

Cross-multiply using the known side-angle pair and retain precision.

04

Solve second side

\[c=200.0720...~m~->~200.1~m\]

Reuse the same known ratio and round only the final value.

05

Submit all fields

\[\text{third}~\text{angle}=C=180-35-72=73~\text{deg};~\text{proportion}=120/\sin35=b/\sin72=c/\sin73;~\text{unknown}~\text{side}~1=b=198.9739...~m~->~199.0~m;~\text{unknown}~\text{side}~2=c=200.0720...~m~->~200.1~m;~\text{tolerance}=±0.05\]

Setup and both numerical outputs are separately scored.

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Another way

  1. Check that the largest computed side lies opposite the largest angle.

!

Common mistake

Do not pair a side with an adjacent rather than opposite angle or stop after one side.

Answer triangle: C=73° and 120/sin(35°) = b/sin(72°) = c/sin(73°); b≈199.0 m and c≈200.1 m.