Seeking to Couble Check My Trig answer?

Question

I'm just trying to make sure I am doing this sort of problem correctly:

The top row of the red seats behind home plate at Cincinnati's Riverfront Stadium is 90 ft. above the level of the playing field. The angle of depression to the base of the left field wall is 14 degrees. How far is the base of the left field wall from a point on the level ground directly below the top row?

tan 14 degrees * 90 ft. equals 22.43952026'

Thanks for any input.

Answer 1

Since tan = O/A, O is 90 and A is unknown.  You would actually need to do 90/tan14 which come out to roughly 361.4.

This would make more sense seeing that the left field wall is probably about 340 feet from home plate, then the additional distance is behind the plate.

Answer 2

I say you are correct if you take the angle of depression from the stands to be 14 degrees therefore your TOA opposite leg is unknown which gives you:

Tan 14 deg = O/90

Opposite = 90* tan 14deg

However it does not make sense to take the angle from the top of the stands therefore take the angle that makes sense; the one that gives you opposite as 90 feet and the adjacent being unknown giving

tan 14 deg = 90/A the more sensible answer...

Answer 3

Should be 90/tan14 = 360.97 feet