Question

A post is supported by two wires (one on each side going in oppositedirections) creating an angle of 80° between the wires. The ends of thewires are 14m apart on the ground with one wire forming an angle of 40°with the ground. Find the lengths of the wires. Put both answersseparated by a comma. (For example 15.11, 19.72) Round to the nearesthundredth.

Answer 1

Using the Sine rule,

`(\sin A)/(A)=(\sin B)/(B)=(\sin C)/(C)`

Hence, the length of wire AP (x) is 9.14m.

For wire BP (y)m,

Sum of angles in a triangle is 180 degrees,

`A^0+P^0+B^0=180^0`
`\begin{gathered} \text{Where A}^0=\text{ unknown,} \\ P^0=80^0\text{ and,} \\ B^0=40^0 \\ A^0+80^0+40^0=180^0 \\ A^0+120^0=180^0 \\ A^0=180^0-120^0 \\ A^0=60^0 \end{gathered}`

Using the side rule to find the length of wire BP,

`\begin{gathered} (\sin 60^0)/(y)=(\sin 80^0)/(14) \\ \text{Crossmultiply,} \\ y*\sin 80^0=14*\sin 60^0 \\ \text{Didive both sides by }\sin 80^0 \\ y=(14*\sin 60^0)/(\sin 80^0) \\ y=12.31m \end{gathered}`

Hence, the length of wire BP (y) is 12.31m

Therefore, the length of the wires are (9.14m and 12.31m).