Question

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 23 feet up. The ladder makes an angle of 75^{\circ}
∘
with the ground. Find the length of the ladder. Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

The length of the ladder that makes an angle of 75 degrees and lies against the wall of a house that's 23 feet tall is approximately 25.88 feet.

The ladder forms a right triangle as it lies against the wall as shown in the image below.

Thus:

x = length of the ladder (hypothenuse)

Reference angle $(\theta) = 75^{\circ}$

25 ft = Opposite

Apply SOH:

Thus,

$sin(\theta) = \frac{Opposite}{Hypotenuse}$

• Plug in the values

$sin(75) = \frac{25}{x}\\\\x = \frac{25}{sin(75)} \\\\\mathbf{x = 25.88}$

Therefore, the length of the ladder that makes an angle of 75 degrees and lies against the wall of a house that's 23 feet tall is approximately 25.88 feet.

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