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TrianglesGeometryHigh schoolabout 1:24

Solve the triangle with sides a = 4, b = 7, c = 9: animated lesson

A narrated, step-by-step triangles video lesson with captions. Final answer: a = 4, b = 7, c = 9; A = 25.2087653°, B = 48.1896851°, C = 106.6015496°; area = 13.41640786, perimeter = 20.

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 sides a = 4, b = 7, c = 9.
2. Step by step
1. $\cos A = \frac{b^2 + c^2 - a^2}{2bc} \Rightarrow A \approx 25.2087653^\circ,\ B \approx 48.1896851^\circ,\ C \approx 106.6015496^\circ$
  Each angle from the law of cosines
2. $\text{Area} = \tfrac12ab\sin C \approx 13.41640786,\ P \approx 20$
  Area and perimeter
3. The answer
$\text{Area} \approx 13.41640786$
area ≈ 13.41640786
4. Check
- Triangle 1: angles sum to 180°; a/sin A = 9.391485505 = c/sin C = 9.391485505.

Transcript

The problem. Here is the problem: Solve the triangle with sides a equals 4, b equals 7, c equals 9. 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 4, b equals 7, c equals 9; A equals 25.2087653°, B equals 48.1896851°, C equals 106.6015496°; area equals 13.41640786, perimeter equals 20. 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 9.391485505 equals c/sin C equals 9.391485505.

About triangles

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

Solve the triangle with sides a = 4, b = 7, c = 9 (Lesson)