Question

Romeo owns a business that puts up and takes down holiday lights. He is working on a house and places the base of his 20-foot ladder at a 4-foot distance from the house. Using the inverse of sine, what is the approximate angle formed where the ladder rests on the house? (1 point)
• 34°
• 90°
• 12°
078°

Answer 1

To find the angle formed by the ladder where it rests against the house, we can use the inverse sine function (arcsin).

We have:
- The length of the ladder (hypotenuse) = 20 feet
- The distance from the base of the ladder to the house (adjacent side) = 4 feet

We can find the height (opposite side) using the Pythagorean theorem first:

\[
\text{height}^2 + 4^2 = 20^2
\]
\[
\text{height}^2 + 16 = 400
\]
\[
\text{height}^2 = 384
\]
\[
\text{height} = \sqrt{384} \approx 19.6 \text{ feet}
\]

Now we can find the angle θ using the sine function:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{19.6}{20}
\]

Now, we take the inverse sine:

\[
\theta = \arcsin\left(\frac{19.6}{20}\right) \approx \arcsin(0.98)
\]

Calculating that gives us an angle approximately equal to:

\[
\theta \approx 78°
\]

So, the approximate angle formed where the ladder rests on the house is **78°**.