To solve this problem, we need to calculate how far away the blood drop landed horizontally from where it was initially found, given the angle of impact and the height above the ground. We can use trigonometric principles to determine this distance.
### Step-by-Step Solution:
1. Understand the problem:
- We are given:
- Angle of impact (θ) = 56 degrees
- Height (h) from which the droplet fell = 5 feet
2. Convert the angle from degrees to radians:
- Trigonometric functions in mathematical calculations use radians. To convert degrees to radians, we use the formula:
[tex]\[
\text{angle\_radians} = \theta \times \left(\frac{\pi}{180}\right)
\][/tex]
- For θ = 56 degrees:
[tex]\[
\text{angle\_radians} = 56 \times \left(\frac{\pi}{180}\right) \approx 0.9774 \text{ radians}
\][/tex]
3. Use the tangent function:
- The tangent of an angle in a right triangle is the ratio of the opposite side (vertical height in this case) to the adjacent side (horizontal distance).
- The tangent function is given by:
[tex]\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
- Rearranging to solve for the horizontal distance (d):
[tex]\[
d = \frac{h}{\tan(\theta)}
\][/tex]
4. Plug in the values:
- Height (h) = 5 feet
- [tex]\(\tan(0.9774) \approx 1.4826\)[/tex]
[tex]\[
d = \frac{5}{1.4826} \approx 3.37 \text{ feet}
\][/tex]
### Conclusion:
The blood drop landed approximately 3.37 feet horizontally away from the point where the bullet hit the person.
