Using the information provided, what is the shadow length (in mm)?

Given:
\[ \tan(\theta) = \frac{\text{length of wedge}}{\text{shadow length}} \]

1. For Altitude: 51.7°
- Length of Wedge: 76 mm

Options:
A. 63.12 mm
B. 61.45 mm
C. 62.58 mm
D. 60.03 mm

2. For Altitude: 65.3°
- Length of Wedge: 76 mm

Options:
A. 34.95 mm
B. 36.12 mm
C. 35.67 mm
D. 33.82 mm

Finding the Altitude and Shadow Length

Data Taken on: August 3, 1997

| Time | Azimuth (from N) | Shadow Length (mm) | Altitude |
|------------|------------------|--------------------|----------|
| 7:30 am | 85 | | |
| 8:40 am | 225 | | |
| 9:35 am | 140 | | |
| 10:45 am | 100 | | 40.2 |
| 12:00 noon | 107.5 | | 51.7 |
| 13:00 pm | 120 | | 37 |
| 13:45 pm | 135 | | 28 |
| 14:30 pm | 150 | | 29 |
| 15:45 pm | 165 | | 65.3 |
| 17:30 pm | 192 | | 53.1 |
| 18:00 pm | 215 | | 109 |
| 18:45 pm | 225 | | 143 |
| 240 | 215 | | |

Please solve for the shadow length using the given values.

The shadow length is calculated using the formula: Shadow length = length of wedge / tan θ. Substituting the given values we get: Shadow length = 76 mm / tan 8. After calculating this, we get the shadow length. The provided altitude doesn’t appear to be used in this calculation.

Explanation:

The shadow length can be calculated using the given formula, tan θ = (length of wedge) / (shadow length). Here, the wedge length is given as 76 mm and tan θ as tan 8. Thus, by rearranging the formula we get shadow length = length of wedge / tan θ. Insert this values into the formula and we have: Shadow length = 76 mm / tan 8. After calculating, the shadow length is obtained.

Also note that, the altitude given (65.3°) does not seem to be relevant to the calculation in this case as the question did not clearly state how it should be used in relation to finding the shadow length.

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