Area from two sides/included angle; Derivation/selection of area formula; Heron rule from three sides; Practical selection of measurements
Example 1
A triangle has sides 10cm and 10cm with included angle 50∘. Find its area. Round to 2 decimal places.
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Answer: 38.30
- Area = ½ab sinC, with C the included angle.
- Rounded result: 38.30.
Example 2
A triangle has sides 9,12,15cm. Find its area using Heron’s rule.
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Answer: 54
- Semiperimeter s=18. Area = √[s(s−9)(s−12)(s−15)]=54.
Example 3
A triangle has area 24cm2, two sides 12cm and 8cm, and acute included angle θ. Find θ in degrees.
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Answer: 30
- Area = ½ab sinθ gives sinθ=21. The acute restriction selects 30∘ rather than 150∘.