A surfer is riding a 7 foot Wave. The angle of depressfon from the surfer to the shorellne Is 10. What is the distance from the sSurfer to the shoreline?

Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
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Chapter2: Right Triangle Trigonometry
Section2.4: Applications
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(#13) I’m so confused, can someone help.
**Trigonometry Problem**

**Question: 15**
A surfer is riding a 7-foot wave. The angle of depression from the surfer to the shoreline is 10°. What is the distance from the surfer to the shoreline?

*Explanation:*
To determine the distance from the surfer to the shoreline, you can use trigonometric principles, particularly the tangent function, which relates the angle of depression to the ratio of the opposite side (height of the wave) over the adjacent side (distance from the surfer to the shoreline). The formula is given by:

\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

In this scenario:
- The opposite side (height of the wave) = 7 feet
- The angle of depression, \( \theta \) = 10°

Rearranging the formula to solve for the adjacent side:

\[ \text{adjacent} = \frac{\text{opposite}}{\tan(\theta)} \]

Substitute the known values into the equation:

\[ \text{adjacent} = \frac{7}{\tan(10°)} \]

Use a calculator to find the value of \( \tan(10°) \):

\[ \tan(10°) \approx 0.1763 \]

Hence:

\[ \text{adjacent} = \frac{7}{0.1763} \approx 39.7 \text{ feet} \]

So, the distance from the surfer to the shoreline is approximately 39.7 feet.
Transcribed Image Text:**Trigonometry Problem** **Question: 15** A surfer is riding a 7-foot wave. The angle of depression from the surfer to the shoreline is 10°. What is the distance from the surfer to the shoreline? *Explanation:* To determine the distance from the surfer to the shoreline, you can use trigonometric principles, particularly the tangent function, which relates the angle of depression to the ratio of the opposite side (height of the wave) over the adjacent side (distance from the surfer to the shoreline). The formula is given by: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] In this scenario: - The opposite side (height of the wave) = 7 feet - The angle of depression, \( \theta \) = 10° Rearranging the formula to solve for the adjacent side: \[ \text{adjacent} = \frac{\text{opposite}}{\tan(\theta)} \] Substitute the known values into the equation: \[ \text{adjacent} = \frac{7}{\tan(10°)} \] Use a calculator to find the value of \( \tan(10°) \): \[ \tan(10°) \approx 0.1763 \] Hence: \[ \text{adjacent} = \frac{7}{0.1763} \approx 39.7 \text{ feet} \] So, the distance from the surfer to the shoreline is approximately 39.7 feet.
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