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)

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°.