Question

A boat is tied to the top of a post on a dock. The rope and the post form a right triangle with the rope as the hypotenuse. The rope is 60 inches long and the post is 3 feet tall. Using the inverse of sine, what is the approximate angle formed between the rope and the post?(1 point)
Responses

37°
37°

48°
48°

87°
87°

53°

Answer 1

To find the angle formed between the rope and the post, we can use the sine function.

In the right triangle formed:
- The opposite side (the height of the post) is 3 feet, which is equivalent to 36 inches (since there are 12 inches in a foot).
- The hypotenuse (the rope) is 60 inches.

We can use the sine function, which is defined as:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Substituting the values we have:
\[
\sin(\theta) = \frac{36}{60}
\]

Now, let's calculate this:
\[
\sin(\theta) = 0.6
\]

To find the angle \(\theta\), we can use the inverse sine function:
\[
\theta = \sin^{-1}(0.6)
\]

Using a calculator to find the angle:
\[
\theta \approx 36.87^\circ
\]

Rounding this value gives us approximately 37°. Therefore, the angle formed between the rope and the post is:

**37°**.