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TrianglesGeometryHigh schoolabout 1:04

Solve the triangle with sides a = 8, b = 15, c = 17: animated lesson

A narrated, step-by-step triangles video lesson with captions. Final answer: a = 8, b = 15, c = 17; A = 28.07248694°, B = 61.92751306°, C = 90°; area = 60, perimeter = 40.

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 = 8, b = 15, c = 17.
2. Step by step
1. $\cos A = \frac{b^2 + c^2 - a^2}{2bc} \Rightarrow A \approx 28.07248694^\circ,\ B \approx 61.92751306^\circ,\ C \approx 90^\circ$
  Each angle from the law of cosines
2. $\text{Area} = \tfrac12ab\sin C \approx 60,\ P \approx 40$
  Area and perimeter
3. The answer
$\text{Area} \approx 60$
area ≈ 60
4. Check
- Triangle 1: angles sum to 180°; a/sin A = 17 = c/sin C = 17.

Transcript

The problem. Here is the problem: Solve the triangle with sides a equals 8, b equals 15, c equals 17. 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 8, b equals 15, c equals 17; A equals 28.07248694°, B equals 61.92751306°, C equals 90°; area equals 60, perimeter equals 40. 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 17 equals c/sin C equals 17.

About triangles

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

Solve the triangle with sides a = 8, b = 15, c = 17 (Lesson)