The extension ladder needs to be about 29.61 feet long to reach the electric box 28 feet up the wall at a 71-degree angle.
A tall house with an electric box 28 feet above the ground.
An extension ladder leaning against the house, reaching the box.
The angle between the ladder and the ground is 71 degrees, forming a right triangle with the house wall as the adjacent side.
Visualizing the right triangle:
We are given the opposite side (28 ft) and need to find the hypotenuse (ladder length). This is where trigonometry comes in!
Using sine function:
The sine function in a right triangle relates the opposite side (opposite angle) to the hypotenuse:
sin(angle) = opposite side / hypotenuse
In our case, the angle is 71 degrees, and the opposite side is 28 feet. Plugging these values into the equation, we get:
sin(71°) = 28 ft / ladder length
Solving for the ladder length:
To find the ladder length, we need to isolate it in the equation. We can do this by rearranging the formula:
ladder length = 28 ft / sin(71°)
Calculating the answer:
Using a calculator, we find that the ladder length is approximately:
ladder length ≈ 29.61 feet
Therefore, the extension ladder needs to be about 29.61 feet long to reach the electric box 28 feet up the wall at a 71-degree angle.