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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 60° with the ground.
Find the length of the ladder. Round your answer to the nearest hundredth of a foot if
necessary

Sagot :

Answer:

32.33 feet

Step-by-step explanation:

In relation to the 60° angle the ladder makes with the ground, the only relevant information we need is that the height from the bottom of the wall to the electric box is 28 feet, which is our opposite side, and we are to find the length of the ladder, which is our hypotenuse. So, we use the sine function.

[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]

[tex]sin60^\circ=\frac{28}{x}[/tex]

[tex]xsin60^\circ=28[/tex]

[tex]x=\frac{28}{sin60^\circ}[/tex]

[tex]x=\frac{28}{(\frac{\sqrt{3}}{2})}[/tex]

[tex]x=\frac{56\sqrt{3}}{3}[/tex] <-- Exact Answer

[tex]x\approx32.33[/tex] <-- Approximate Answer

Therefore, the length of the ladder is about 32.33 feet.

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