Hello, My name is Suhana, and I'm a local detective. Today, I will solve a mystery using trigonometric functions.
I'm standing 20 feet away from the building, and looking up at a 45 degree angle. The distance from me to the top of the building is 20/cos45, which is about 28.3 feet.
There was a report about a gunshot here just recently. This building is abandoned, but the investigative team found a bullet inside.
We are on the third floor. The bullet we are examining went through the window, and then hit the wall inside. We measured the distance from one bullet hole to another, and we found it traveled 13 feet.
Using sin^-1 (12/13)= about 67.4 degrees, we find the angle the bullet was shot at. The angle of elevation is 90 - 67.4 = 22.6 degrees.
The distance from one wall to another is 12 feet. Using this information, we can find the angle of the bullet.
tan x = o/a; tan(22.6)=19/a.a = 19/tan 22.6 = about 45.6 feet.
Now we're at the shop across the street. We are waiting for the manager to return with some tapes. Meanwhile, we are trying to figure out where the shooter was standing when they shot. The bullet was found 19 feet up, and we know the angle the bullet was shot at, we can find the distance quite easily.
Wait a second...I think I hear something.....
We quickly barged in on the manager, who was destroying the security camera records. The policeman who I called with me was obviously confused as to how I knew he was the culprit, but arrested him nonetheless. Since the place where the shooter was standing was inside this shop, it could only be the manager.
Since no one was harmed, I don't think he will get a harsh charge, but he will certainly get a warning. That is how we can utilize trigonometric functions to solve mysteries.