Question

A flag pole has a rope that attaches to the ground from the top of the flagpole the rope create a 30° angle with the ground and is attached 10 m from the bottom of the pool how long is the rope in how tall is the flagpole

Answer 1

`5.77\ \text{m}`

`11.54\ \text{m}`

Explanation:

p = Height of pole

h = Length of role

b = Distance between the bottom of the rope and bottom of the pole = 10 m

`\theta` = Angle between the rope and the ground =
`30^(\circ)`

`\tan\theta=(p)/(b)\\\Rightarrow p=b\tan\theta\\\Rightarrow p=10\tan30^(\circ)\\\Rightarrow p=5.77\ \text{m}`

The length of the rope is
`5.77\ \text{m}`

`\cos\theta=(b)/(h)\\\Rightarrow h=(b)/(\cos\theta)\\\Rightarrow h=(10)/(\cos30^(\circ))\\\Rightarrow h=11.54\ \text{m}`

The length of the pole is
`11.54\ \text{m}`