Phsyics problem. I must find distance in Kilometers.

afcwestwarrior

1. The problem statement, all variables and given/known data
You are driving into St.Louis Missouri, and in the distance you see the famous Gateway-to-the-west arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 2.0 degrees above the horizontal. Approximately how far (In Kilometers) are you from the base of the arch.


Height= 192 m
Angle= 2.0 degrees

[b]2. Relevant equations[/b
Definition of Cos, Sin, and Tan or the inverse trigonometric functions


I have no clue on what I should do.
This is what I did.
H adjacent= 192/tan(2.0)= 5498m and then I converted it to KM and I got 8848 km. This answer is way off, and I know I'm doing something wrong.

Mindscrape

You did the equation right.

tanØ = y/x

x = height/tan2

x = 5498m

How many meters are in a kilometer?

Dick

You were doing great until you tried to convert the units. What strange conversion formula are you using? m -> km just involves dividing by 1000.

afcwestwarrior

1,000 meters equal 1 kilometer, oh no wonder I had a reference sheet that said 1 KM equals .6214 Meters. Ok so the answer is 5.498. Thank you for helping me out.

Dick

km=0.6214 MILE. I wouldn't use the same abbreviation for meter and mile!

afcwestwarrior

Oh lol no wonder. In my conversion factor reference it just had m as the symbol, so it confused me.

Mindscrape

Remember, it is a KILOmeter. Kilo means 10^3, so 1000meter. ;)