Answered

IDNLearn.com provides a seamless experience for finding and sharing answers. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 31 feet up. The ladder makes an angle of 63∘∘ with the ground. Find the length of the ladder. Round your answer to the nearest hundredth of a foot if necessary.

Sagot :

Explanation

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]Answer

The length of the ladder is 34.79 ft to the nearest hundred.

View image AlyssandraG684414
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.