I am currently in a pre-calculus class at school. The problem below came from a "Right Triangle Trig Challenge Problems" worksheet. I solved all the other problems, but cannot figure this one out. The teacher said he originally thought it was a trig problem, but later realized it was just geometry. I think he may have been mistaken. Either way, I was never good at geometry, so it's not a surprise I can't figure it out. The problem is graphical, so I attempted to recreate it using Paint, thinking it'd be clearer than my explanation. I didn't see anything against posting links in the forum rules, so if you will, please check out the imageshack link below to see the problem:
http://img152.imageshack.us/img152/2419/trigms9.jpg
Ignore the incorrect scale, please. I don't know how to create an image to scale on a computer. Also, measurements are in feet.
Now, on to what I've done:
Using the knowledge that it's a 3-4-5 triangle, I labeled one of the diagonals as 50 ft. Next, I found all the angles in the diagram. I also split the triangle with hypotenuse of 40 into two right triangles for clarification. I found the lower (after intersection) segment of the larger diagonal using:
sin(53)=opposite/30
opposite=30sin(53)
Approx. = 23.959
BUT, using Pythagorean theorem I found the length of the larger diagonal to be the square root of 8000, or about 89.443.
When I use sin(53)=opposite/80
opposite=80sin(53)
Approx. = 63.891
89.443 - 63.891 doesn't equal anything close to 23.959. It equals about 25.552
Wait - I just saw that I used that second sine equation on a non-right triangle. We haven't learned that yet. Probably why it's wrong.
I don't know how to solve this. Any help would be appreciated.
http://img152.imageshack.us/img152/2419/trigms9.jpg
Ignore the incorrect scale, please. I don't know how to create an image to scale on a computer. Also, measurements are in feet.
Now, on to what I've done:
Using the knowledge that it's a 3-4-5 triangle, I labeled one of the diagonals as 50 ft. Next, I found all the angles in the diagram. I also split the triangle with hypotenuse of 40 into two right triangles for clarification. I found the lower (after intersection) segment of the larger diagonal using:
sin(53)=opposite/30
opposite=30sin(53)
Approx. = 23.959
BUT, using Pythagorean theorem I found the length of the larger diagonal to be the square root of 8000, or about 89.443.
When I use sin(53)=opposite/80
opposite=80sin(53)
Approx. = 63.891
89.443 - 63.891 doesn't equal anything close to 23.959. It equals about 25.552
Wait - I just saw that I used that second sine equation on a non-right triangle. We haven't learned that yet. Probably why it's wrong.
I don't know how to solve this. Any help would be appreciated.