Answer:
36.65 ft (2 dp)
Step-by-step explanation:
- Angles around a point sum to 360°
- 1 hour = 60 minutes
Therefore, the minute hand of a clock travels 360° in 60 minutes
Number of degrees the minute hand will travel in 25 minutes:
[tex]\sf =\dfrac{360}{60} \times 25=150^{\circ}[/tex]
To find how far the tip of the minute hand travels in 25 minutes, use the Arc Length formula:
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Given:
- r = length of minute hand = 14 ft
- [tex]\theta[/tex] = 150°
[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (14)\left(\dfrac{150^{\circ}}{360^{\circ}}\right)\\ & = 28\pi \left(\dfrac{5}{12}\right)\\ & = \dfrac{35}{3} \pi \\ & = 36.65\: \sf ft\:(2\:dp)\end{aligned}[/tex]
