Solve a problem

TrianglesGeometryHigh schoolabout 1:03

Solve the triangle with sides a = 3, b = 4, c = 5: animated lesson

A narrated, step-by-step triangles video lesson with captions. Final answer: a = 3, b = 4, c = 5; A = 36.86989765°, B = 53.13010235°, C = 90°; area = 6, perimeter = 12.

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 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Solve the triangle with sides a = 3, b = 4, c = 5.
2. Step by step
1. $\cos A = \frac{b^2 + c^2 - a^2}{2bc} \Rightarrow A \approx 36.86989765^\circ,\ B \approx 53.13010235^\circ,\ C \approx 90^\circ$
  Each angle from the law of cosines
2. $\text{Area} = \tfrac12ab\sin C \approx 6,\ P \approx 12$
  Area and perimeter
3. The answer
$\text{Area} \approx 6$
area ≈ 6
4. Check
- Triangle 1: angles sum to 180°; a/sin A = 5 = c/sin C = 5.

Transcript

The problem. Here is the problem: Solve the triangle with sides a equals 3, b equals 4, c equals 5. Side a is opposite angle A, b opposite B and c opposite C. This is the SSS case.

Step by step. Each angle from the law of cosines. Area and perimeter.

The answer. So the answer is a equals 3, b equals 4, c equals 5; A equals 36.86989765°, B equals 53.13010235°, C equals 90°; area equals 6, perimeter equals 12. 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 5 equals c/sin C equals 5.

About triangles

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

Solve the triangle with sides a = 3, b = 4, c = 5 (Lesson)