Question

At an average walking speed of 2 m/s, how many minutes will it take a hiker to make a complete circuit around the triangular trail? Round to the nearest minute.

Answer 1

From the triangle, we need to first of all calculate the value of m

To do that, we apply cosine rule

`\begin{gathered} a^2=b^2+c^2-2bc\cos A\ldots\ldots\ldots\ldots\ldots.co\sin e\text{ rule} \\ m^2=410^2+200^2-2(410)(200)\cos 100 \\ m^2=168100+40000-164000\text{ x -0.173648} \\ m^2=\text{ 236578.3} \\ m=\sqrt[]{236578.3} \\ m\text{ = 486.4 m} \end{gathered}`

Total distance cycled = 486.4m + 410m + 200m = 1096.4m

`\begin{gathered} \text{But average speed = }\frac{\text{total distance covered , s}}{\text{total time take, t}}\text{ } \\ \\ 2\text{ = }(1096.4)/(t) \\ 2t=1096.4 \\ t\text{ =}(1096.4)/(2) \\ t=\text{5}48.2s \end{gathered}`
`\begin{gathered} \text{converting 548.2s to minutes, we have } \\ t=(548.2s)/(60s) \\ t=9.137\text{ minutes} \\ t=\text{ 9 minutes (nearest minute)} \end{gathered}`