lenth of side of a tri are 6in8in12in area tri round to nearest tenth

Question

the length of the sides ofatriangle are 6in 8in 12in. find the area ofthe triangle round to the nearest tenth

Answer 1

We can use the cosine rule to find an angle θ:

12²=6²+8²-2(6)(8)cosθ, [cosine rule is c²=a²+b²-2abcosC, so a=6in, b=8in, c=12in, C=θ]

144=36+64-96cosθ,

96cosθ=44, cosθ=11/24,

We need sinθ=√(1-cos²θ)=√455/24, [area=½absinC, a=6in, b=8in, C=θ].

area=½(6)(8)sinθ=√455=21.3in² to the nearest tenth of an inch.