Finding the Angle of Elevation

Question

I wish I could add a picture on here to properly explain what I am trying to do. I got a picture with a problem, so I'll try to explain it.

There's a 140 foot tree that is on a sloped price of property and casts a shadow of 200 feet. The angle of elevation of the sun is 38 degrees. I need to find the angle of elevation of the sloped ground.

There is a slanted line, going upward left to right, which is the hill I'm talking about. In the middle of the line is the tree. To the right of the line is the sun, so I drew an imaginary horizontal line (from the bottom of the tree) so that I could put the 38 degree angle of elevation up to the sun. When I was doing the problem, I drew a horizontal line from the bottom left of the shadow (going right), and put theta in that corner because that would be the angle of elevation I need. I also took the 38 degree line down past where I originally put it an connected it to the bottom on the horizontal line, meaning that the second angle in the triangle would be 142 degrees (180 - 38). So now for the top of the triangle I have the 200 feet, and I have the middle angle of 142 degrees. I need a way to either get a side or to get another angle. I guess I just don't understand how I'm supposed to get the angle of elevation this way, I think I am doing it wrong but I don't know.

Any help would be appreciated. Thanks in advance.

Answer 1

Mark the tip of the tree "t"

sin t / 200 = sin 38° / 140

sin t = 200 sin 38° / 140

sin t = 0.8795

t = 61.584º

θ = 90° - 38° - 61.584°

θ = -9.584 Now that is impossible. I checked by arithmetic several times (still could have missed something).