Question

A rescuer is trying to save a cat at the very top of a tree. The height of the tree is 35 feet. A rope is thrown to the top of the tree at a 25° angle from a tether on the ground.

1. Draw a diagram to model the problem.

2. What is the length of the rope needed to meet the tree? Show all work and label the answer. Round to the nearest tenth, if needed.

Answer 1

$\sin(c) = \frac{opposite}{hypotenuse}$

$\sin(25) = \frac{35}{b}$

$(b) \sin(25) = \frac{35}{b}(b)$

$(b) \sin(25) = 35$

$\frac{(b) \sin(25) }{ \sin(25) } = \frac{35}{ \sin(25) }$

$b = \frac{35}{ \sin(25) }$

$b = 82.8$

the length of the rope needs to be around 82.8