crime find a bullet hole in a wall at a height of 7 ft 6 in. from the floor. how far away from the wall was the gun when it was fired?

Question

Detectives investigating a crime find a bullet hole in a wall at a height of 7 ft 6 in. from the floor. Since the bullet passed through the wall at an angle of 34°, detectives know that the gun was fired at an angle of 34°. If they assume that the gun was fired from a height of 4 ft above the floor, how far away from the wall was the gun when it was fired? (Round to the nearest foot.)

Answer 1

There is a right triangle formed from where the shooter was from the wall and where the bullet was hole was.

 

This triangle has a height of the difference of where the bullet was found (7.5 ft) and the height the gun was fired (4 ft).  This difference is 3.5 ft.

 

Let x be distance the gun was when the gun was fired, and 34° the angle the gun was fired.

 

Then tan(34) = 3.5/x => x = 3.5/tan/(34) ≈5.2 ft