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TrianglesGeometryHigh schoolabout 1:22

Solve the triangle with A = 40°, B = 60° and c = 10: animated lesson

A narrated, step-by-step triangles video lesson with captions. Final answer: a = 6.527036447, b = 8.793852416, c = 10; A = 40°, B = 60°, C = 80°; area = 28.26289687, perimeter = 25.32088886.

SpeedLanguage

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 = 40°, B = 60° and c = 10.
2. Step by step
1. $C = 180^\circ - 100^\circ = 80^\circ$
  Third angle from the angle sum
2. $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \Rightarrow a \approx 6.527036447,\ b \approx 8.793852416,\ c \approx 10$
  Remaining sides from the law of sines
3. $\text{Area} = \tfrac12ab\sin C \approx 28.26289687,\ P \approx 25.32088886$
  Area and perimeter
3. The answer
$\text{Area} \approx 28.26289687$
area ≈ 28.26289687
4. Check
- Triangle 1: angles sum to 180°; a/sin A = 10.15426612 = c/sin C = 10.15426612.

Transcript

The problem. Here is the problem: Solve the triangle with A equals 40°, B equals 60° and c equals 10. 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 6.527036447, b equals 8.793852416, c equals 10; A equals 40°, B equals 60°, C equals 80°; area equals 28.26289687, perimeter equals 25.32088886. 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 10.15426612 equals c/sin C equals 10.15426612.

About triangles

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

Solve the triangle with A = 40°, B = 60° and c = 10 (Lesson)