From the statement, we know that:
• the ladder reaches an electric box 31 ft up,
,• the ladder makes an angle of 63° with the ground.
Using these data, we make the following diagram:
From the diagram, we see that the ladder and the wall form a right triangle with:
• H = hypotenuse = length of the ladder,
,• OS = opposite side to angle θ = 31 ft,
,• θ = angle between the ladder and the ground = 63°,
From trigonometry, we have the following trigonometric relation between H, OS and θ:
[tex]\sin\theta=\frac{OS}{H}.[/tex]Replacing the data from above and solving for H, we get:
[tex]\begin{gathered} \sin(63\degree)=\frac{31ft}{H}, \\ H\cdot\sin(63\degree)=31ft, \\ H=\frac{31ft}{\sin(63\degree)}\cong34.79ft. \end{gathered}[/tex]AnswerThe length of the ladder is 34.79 ft to the nearest hundred.
