GOZUNTA
Try it now
All courses Geometry · G-SRT.11 56 of 57
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
For the triangle shown, \(a~=~120~m\), \(A~=~35°\), and \(B~=~72°\). Find \(C\), then use the Law of Sines to find \(b\) and \(c\).
Prompt triangle with A=35°, B=72°, and side a=120 m; C and sides b and c are withheld. Open full size
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Stop now. Continue later.

A saved learning session lets you leave when you need to and return without losing your place.

Create a free account
With paid access

Use the screen to choose. Use paper to solve.

Build the exact session you want online, then export it as a printable worksheet.

Compare plans

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 the third angle

\[C=180^{\circ}-35^{\circ}-72^{\circ}=73^{\circ}\]

Triangle angles sum to 180 degrees.

02

Build matched sine ratios

\[120/\sin(35^{\circ})=b/\sin(72^{\circ})=c/\sin(73^{\circ})\]

Side a=120 is opposite A=35 degrees, anchoring both unknown-side proportions.

03

Solve the unknown sides

\[b=120\sin(72^{\circ})/\sin(35^{\circ})~\text{approx}~199.0~m;~c=120\sin(73^{\circ})/\sin(35^{\circ})~\text{approx}~200.1~m\]

Keep full calculator precision until rounding each final length to the tenth.

04

Check and conclude

\[C=73^{\circ}.~\text{From}~120/\sin(35^{\circ})~=~b/\sin(72^{\circ})~=~c/\sin(73^{\circ}),~b~\text{approx}~199.0~m~\text{and}~c~\text{approx}~200.1~m.\]

The angle order 35<72<73 agrees with the side order 120<199.0<200.1.

+

Another way

  1. Calculate the common scale factor 120/sin35, then multiply it by sin72 and sin73.

!

Common mistake

Do not pair 120 with 72 degrees. Lowercase side a is opposite capital angle A=35 degrees.

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

Solution walkthrough video