Question

The backyard of a house is in the shape of a triangle with two sides measuring 18.3 m and 12.1 m and the angle between these two sides is 32.7°Find the length of the third side of the triangle.

Answer 1

Step 1

Draw the back yard.

Step 2

State cosine rule

`a^2=c^2+b^2-2cb\cos A`
`\begin{gathered} A=32.7^(\circ) \\ a=\text{ third side} \\ b=18.3 \\ c=12.1 \end{gathered}`

`a=\sqrt[]{12.1^2+18.3^2-2(12.1)(18.3)(\cos 32.7)}`
`\begin{gathered} a=\sqrt[]{146.41+334.89-372.6714649} \\ a=\sqrt[]{481.3-372.6714649} \\ a=\sqrt[]{108.6285351} \\ a=10.42250138 \\ a\approx10.42m\text{ to the nearest hundredth} \end{gathered}`

Hence the length of the third side is approximately 10.42m to the nearest hundredth.