Question

Solve triangles using the law of cosines . Find BC

Answer 1

The cosine rule states that:

`a^2=b^2+c^2-2bc\cos A`

For the given triangle:

a= BC

b=AC=12

c=AB=9

∠A=87º

Replace the known measures on the formula:

`BC^2=12^2+9^2-2(9\cdot12\cdot\cos 87)`

Solve the exponents and the multiplication on the last term:

`\begin{gathered} BC^2=144+81-216\cos 87 \\ BC^2=213.695 \end{gathered}`

-Apply the square root to both sides of the expression:

`\begin{gathered} \sqrt[]{BC^2}=\sqrt[]{213.695} \\ BC=14.618 \\ BC\approx14.62 \end{gathered}`

The length of side BC is 14.62units