what is the area of a triangle with 5, 16, 12

Question

i really need help on this!!!!

Answer 1

We can use the Cosine Rule to find an angle:

Let a=5, b=16, c=12 then a²=b²+c²-2bccosA,

cosA=(b²+c²-a²)/(2bc)=(256+144-25)/(384)=375/384=125/128=0.9765625, A=12.4293° approx.

Area of triangle=½bcsinA=96×0.2152=20.66 square units or 96√(1-cos²A).

As a formula we could have written:

Area=½bc√(1-(b²+c²-a²)²/(4b²c²))=¼√(4b²c²-(b²+c²-a²)²).