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TrianglesGeometryHigh schoolabout 1:27

Solve the triangle with A = 35°, B = 75° and c = 12: animated lesson

A narrated, step-by-step triangles video lesson with captions. Final answer: a = 7.324647533, b = 12.33500153, c = 12; A = 35°, B = 75°, C = 70°; area = 42.45039732, perimeter = 31.65964906.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.5 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Solve the triangle with A = 35°, B = 75° and c = 12.
2. Step by step
1. $C = 180^\circ - 110^\circ = 70^\circ$
  Third angle from the angle sum
2. $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \Rightarrow a \approx 7.324647533,\ b \approx 12.33500153,\ c \approx 12$
  Remaining sides from the law of sines
3. $\text{Area} = \tfrac12ab\sin C \approx 42.45039732,\ P \approx 31.65964906$
  Area and perimeter
3. The answer
$\text{Area} \approx 42.45039732$
area ≈ 42.45039732
4. Check
- Triangle 1: angles sum to 180°; a/sin A = 12.77013327 = c/sin C = 12.77013327.

Transcript

The problem. Here is the problem: Solve the triangle with A equals 35°, B equals 75° and c equals 12. Side a is opposite angle A, b opposite B and c opposite C. This is the ASA case.

Step by step. Third angle from the angle sum. Remaining sides from the law of sines. Area and perimeter.

The answer. So the answer is a equals 7.324647533, b equals 12.33500153, c equals 12; A equals 35°, B equals 75°, C equals 70°; area equals 42.45039732, perimeter equals 31.65964906. Three measurements including a side normally fix a triangle. Two sides with a non-included angle (SSA) can give zero, one or two triangles.

Check. Triangle 1: angles sum to 180°; a/sin A equals 12.77013327 equals c/sin C equals 12.77013327.

About triangles

Solve triangles with the law of sines and the law of cosines, and find their area.

Solve the triangle with A = 35°, B = 75° and c = 12 (Lesson)