BUILD FLUENCY. EARN YOUR ASCENT.Sign in Year 11 · General Mathematics
Solving problems with non-right triangles
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Solving problems with non-right triangles
Cosine rule for side or angle; Sine rule for AAS/ASA and SSA; Ambiguous cases; Direction and bearings
Example 1
In a triangle, side a=8cm is opposite 40∘, and side b is opposite 65∘. Find b. Round to 2 decimal places.
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Answer: 11.28
- Use sin65∘b=sin40∘a.
- Rounded result: 11.28.
Example 2
Two sides are 8cm and 6cm with included angle 60∘. Find the opposite third side. Round to 2 decimal places.
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Answer: 7.21
- Cosine rule: c2=a2+b2−2ab cos60∘.
- Rounded result: 7.21.
Example 3
A triangle has sides 6,6,6cm. Use the cosine rule to find any angle, in degrees.
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Answer: 60
- Cos θ=2a2a2+a2−a2=21, so θ=60∘.
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