an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric…

an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 28 feet up. the ladder makes an angle of 71° with the ground. find the length of the ladder. round your answer to the nearest hundredth of a foot if necessary.

an electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 28 feet up. the ladder makes an angle of 71° with the ground. find the length of the ladder. round your answer to the nearest hundredth of a foot if necessary.

Answer

Answer:

(29.70) feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the height (opposite side to the given angle) (y = 28) feet and the angle (\theta=71^{\circ}), and we want to find the length of the ladder (hypotenuse) (x). Using the sine function (\sin\theta=\frac{y}{x}).

Step2: Solve for (x)

Since (\sin\theta=\frac{y}{x}), we can rewrite it as (x = \frac{y}{\sin\theta}). Substituting (y = 28) and (\theta = 71^{\circ}), and knowing that (\sin(71^{\circ})\approx0.9455), we get (x=\frac{28}{\sin(71^{\circ})}=\frac{28}{0.9455}\approx29.70) feet.