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Mathematics Worksheet
📐 Law of Cosines
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Apply c2 = a2 + b2 − 2ab·cos C.Find a side from two sides and the included angle (SAS).Find an angle from three sides (SSS).Relate it to the Pythagorean theorem.📚 Quick Recap
The Law of Cosines generalizes the Pythagorean theorem to work with ANY triangle, not just right triangles — essential when you know sides but not a convenient right angle.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1A triangle has a=8, b=15, C=90°. Side c is:
2A triangle has a=6, b=7, c=9. cos C is about:
3Using that, angle C is about:
4The Law of Cosines is used with:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Law of Cosines: c2 = a2 + b2 − .
6When C = 90°, cos C = 0, so it reduces to the theorem.
7A triangle has a=8, b=15, C=90°. Find c.
8A triangle has a=5, b=9, C=45°. Find c2.
9A triangle has sides a=6, b=7, c=9. Find cos C.
🚀 Section C · Challenge ● CHALLENGE 5
10Using the previous result, find angle C.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 2ab·cos C 6 Pythagorean 7 = 17 (matches the Pythagorean theorem) 8 = 106 − 63.64 ≈ 42.36 9 = 4/84 ≈ 0.048 | 10 = arccos(0.048) ≈ 87.3°