Question

An electrician leans an extension ladderagainst the outside wall of a house so thatit reaches an electric box 29 feet up. Theladder makes an angle of 71 degreeswith the ground. Find the length of theladder. Round your answer to the nearesttenth of a foot if necessary.

Answer 1

`30.7\:ft^`

1) We can sketch this out to better grasp it:

Since the height is always perpendicular, so we can tell that this is a right angle and the ladder is the hypotenuse.

2) So now, we can make use of one trig ratio that relates the opposite leg to angle 71º and the hypotenuse:

`\begin{gathered} \sin(71^(\circ))=(29)/(ladder) \\ \\ ladder=(29)/(\sin(71)) \\ ladder\approx30.7\:ft \\ \end{gathered}`

So the ladder is 30.7 ft long.