The Sine and Cosine Ratios Quick Check

Question

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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

22.0
feet
22 point 0 feet

16.5
feet
16 point 5 feet
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Answer 1

To find the height of the tower above Ella's eye level using the sine ratio, we can set up the problem using the sine function.

The sine ratio is defined as: $$\sin (\text{angle})=\frac{\text{opposite}}{\text{hypotenuse}}$$

In this scenario:

• The angle is 21°.
• The opposite side is the height of the tower above Ella's eye level (let's call this $h$).
• The hypotenuse is the direct distance from her eyes to the top of the tower, which is 46 feet.

So the sine ratio can be set up as: $$\sin (21°)=\frac{h}{46}$$

To solve for $h$, you multiply both sides by 46: $$h=46\cdot \sin (21°)$$

Now, calculating this gives: $$h\approx 46\cdot 0.3584\approx 16.5\text{ feet}$$

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

To find the total height of the tower, you would then need to add Ella's eye level (5.5 feet) to this result: $$\text{Total height}=h+5.5=16.5+5.5=22\text{ feet}$$

The correct response that uses the sine ratio to find the height above Ella's eye level is: 16.5 feet.