Question

Ella is standing on the ground, looking up toward the top of a tower. Her eye level is 5.5
feet above the ground, and her sightline forms a 21°
degree angle while looking at the top of the tower. The direct distance from her eyes to the top of the tower is 46 feet.

Which of the following correctly uses the sine ratio to find the height of the tower?

(1 point)
Responses

128.4
feet
128 point 4 feet

42.9
feet
42 point 9 feet

16.5
feet
16 point 5 feet

22.0
feet

Answer 1

To find the height of the tower above Ella's eye level using the sine ratio, we can use the formula:

\[
\text{sine(angle)} = \frac{\text{opposite side}}{\text{hypotenuse}}
\]

In this context:

- The "angle" is 21° (the angle of elevation).
- The "opposite side" is the height of the tower above Ella's eye level, which we can call \( h \).
- The "hypotenuse" is the direct distance from her eyes to the top of the tower, which is 46 feet.

Using the sine ratio, we have:

\[
\sin(21°) = \frac{h}{46}
\]

To find \( h \), we can rearrange the equation:

\[
h = 46 \cdot \sin(21°)
\]

Now we can calculate \( h \):

1. Calculate \( \sin(21°) \) (approximately 0.3584).
2. Multiply by 46:

\[
h \approx 46 \cdot 0.3584 \approx 16.5 \text{ feet}
\]

So the height of the tower above Ella's eye level is approximately 16.5 feet.

Adding Ella's eye level to find the total height of the tower:

- Ella's eye level is 5.5 feet.
- Total height = 16.5 feet + 5.5 feet = 22.0 feet.

Therefore, the correct response that uses the sine ratio to find the height above Ella's eye level is:

**16.5 feet**.