Question

A cat climbs on top of a house and looks down at you. You are standing 10 feet away from the house and there is an 18-foot diagonal distance between you and the cat. Find the angle between the side of the house and the cat's line of sight looking down at you. Round your answer to the nearest whole number.

18 is the hypotenuse while 10 is the opposite

(1 point)
Responses

34 degrees
34 degrees

42 degrees
42 degrees

48 degrees
48 degrees

56 degrees
56 degrees
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Answer 1

To find the angle between the side of the house and the cat's line of sight, we can use the sine function, as we have the opposite side (the distance from the base of the house to where you are standing) and the hypotenuse (the diagonal distance from the cat down to you).

We can use the formula for sine:

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

In this case:

- Opposite = 10 feet
- Hypotenuse = 18 feet

Plugging these values into the formula gives us:

\[
\sin(\theta) = \frac{10}{18} = \frac{5}{9}
\]

Now we need to find the angle \( \theta \):

\[
\theta = \arcsin\left(\frac{5}{9}\right)
\]

Calculating this using a calculator:

\[
\theta \approx 34.95 \text{ degrees}
\]

Rounding this to the nearest whole number gives us:

\[
\theta \approx 35 \text{ degrees}
\]

However, in the context of the options provided (34 degrees, 42 degrees, 48 degrees, 56 degrees), the closest is:

**34 degrees**.