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Trigonometry: The Area of a Triangle given 3 sides
If the sides of a triangle are 4cm, 3.9cm and 6.6cm,
then its area to 3 dps is cm2

tickcross



Worked Solution

If we know angle A and the two sides b and c next to that angle, then we can use:
The Triangle Area formula: Area =
bc sin(A)
---
2
We can compute one angle given 3 sides as follows:
Cosine Rule: a2 = b2 + c2 – 2 bc cos(A)  or  cos(A) =
b2 + c2 – a2
---
2 bc

Let a = 4, b = 3.9 and c = 6.6. The Cosine Rule for cos(A) gives:
cos(A) =
3.92 + 6.62 – 42
---
2×3.9×6.6
 = 0.83081 so A = 33.818°

Use this angle value in the Triangle Area formula to find the area:
Area =
3.9 × 6.6 sin( 33.818°)
---
2
 = 7.163 to 3 dps.
C

   
3.9 4
A6.6B
not to scale

© MEI Produced by Dr Ron Knott, revised 30 April 2008
tom . button [AT] mei . org . uk 		Test reference: TrigTriAreaSSS.html?ref=34757