Question

Gunmen shoot a victim who is 5.9 feet tall from the roof of a building 268.5 feet away. If the roof of the building were 385 feet high, at what angle to the horizon would the bullet have been fired?

A) 11.3 degrees
B) 22.6 degrees
C) 34.1 degrees
D) 45.4 degrees

Answer 1

The angle to the horizon would be calculated using the inverse tangent function with the height difference between the gun and the victim as the opposite side, and the distance to the victim as the adjacent side.

Step-by-step explanation:

The student's question involves calculating the angle of a projectile (in this case, a bullet) given its target height and horizontal distance. This problem is solved using the principles of trigonometry and projectile motion in physics. To calculate the angle of elevation, we use the tangent function, which is the ratio of the opposite side to the adjacent side of a right triangle. Here, the opposite side is the height difference between the gun and the victim (385 feet - 5.9 feet) and the adjacent side is the horizontal distance of 268.5 feet.

To find the angle, we solve for θ in the following equation:
tan(θ) = opposite/adjacent, which translates to tan(θ) = (385 - 5.9) / 268.5. Once we calculate the inverse tangent (arctan) of that ratio, we obtain the angle of elevation in degrees.