A bullet hole in the wall at height of 7'6 inches from the floor. Bullet passed through wall at angle 34 degrees. If they assume that the gun was fired from a height 4' above the floor, how far away from the wall was it when it was fired? (nearest inch)
To determine the horizontal distance the bullet was from the wall when it was fired, you can use trigonometry. Here's how you can find the answer:
1. Convert the height of the bullet hole from feet and inches to inches. Since there are 12 inches in a foot, 7 feet would be equivalent to 7 x 12 = 84 inches. Therefore, the height of the bullet hole is 84 + 6 = 90 inches.
2. Convert the height of the gun from feet and inches to inches. 4 feet is equal to 4 x 12 = 48 inches.
3. Calculate the vertical component of the bullet's path by subtracting the height of the gun from the height of the bullet hole: 90 - 48 = 42 inches.
4. Convert the angle from degrees to radians by dividing it by 180 and multiplying by π (pi). 34 degrees is approximately 34/180 * π = 0.5934 radians.
5. Use the trigonometric function tangent (tan) to calculate the horizontal distance (x) between the gun and the wall: tan(angle) = vertical distance / horizontal distance. In this case, tan(0.5934) = 42 / x.
6. Rearrange the equation to solve for x: x = 42 / tan(0.5934).
7. Plug this equation into a calculator or use trigonometric tables to find the value of x. This would give you the horizontal distance, measured in inches, between the gun and the wall when it was fired.
8. Round the result to the nearest inch for the final answer.
Please note that if you do not have access to a calculator or trigonometric tables, you can use online trigonometry calculators or software to easily obtain the answer.