SOLUTION: A flagpole is supported by two guy wires on opposite sides. The wires are 35.3 feet and 36.9 feet long and anchored to the ground 56.9 feet apart. What angles do the wires make wit

Algebra ->  Trigonometry-basics -> SOLUTION: A flagpole is supported by two guy wires on opposite sides. The wires are 35.3 feet and 36.9 feet long and anchored to the ground 56.9 feet apart. What angles do the wires make wit      Log On


   

Question 1035358: A flagpole is supported by two guy wires on opposite sides. The wires are 35.3 feet and 36.9 feet long and anchored to the ground 56.9 feet apart. What angles do the wires make with the ground?
Thank you so much :)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter of the triangle: 35.3%2B36.9%2B56.9=35.3%2B36.9%2BL%2Br
Along the ground: L%2Br=56.9

Triangle Area: %281%2F2%29%2A%2856.9%29=%281%2F2%29%28L%2Br%29, or 56.9=L%2Br

Only one equation for that much, being highlight_green%28L%2Br=56.9%29.

The left and right side triangles each are Right triangles with height h.
system%28h%5E2%2BL%5E2=35.3%5E2%2Ch%5E2%2Br%5E2=36.9%5E2%29

Equating h^2:
35.3%5E2-L%5E2=36.9%5E2-r%5E2
35.3%5E2-L%5E2%2Br%5E2=36.9%5E2
r%5E2-L%5E2=36.9%5E2-35.3%5E2
r%5E2-L%5E2=1361.61-1246.09
r%5E2-L%5E2=115.52

Summarizing as a system of equations
system%28L%2Br=56.9%2Cr%5E2-L%5E2=115.52%29
-
What to do next is solve this system for L and r;
and then use simple trigonometry to find the angles asked. Cosines would be best.