SOLUTION: It is desired to draw a triangle so that the first angle is 5/4 of the second but is greater than the third by 40. What should be the magnitudes of the angles of the triangle? t

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Question 346019: It is desired to draw a triangle so that the first angle is 5/4 of the second but is greater than the third by 40. What should be the magnitudes of the angles of the triangle?
thank you!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the 1st angle, let y = the 2nd angle, let z = the 3rd angle
:
Write an equation for each phrase
;
" draw a triangle so that the first angle is 5/4 of the second"
x = 5%2F4y
Multiply both sides by 4
4x = 5y
divide both sides by 5
4%2F5x = y
or we can just write it:
y = .8x
:
"but is greater than the third by 40."
z = x - 40
;
x + y + z = 180
Replace y with .8x; replace z with (x-40)
x + .8x + x - 40 = 180
2.8x = 180 + 40
x = 220%2F2.8
x = 78.57 degrees is the 1st angle
and
.8(78.57) = 62.65 degrees is the 2nd angle
and
78.57-40 = 38.57 degrees is the 3rd angle
:
:
Check solution
78.57 + 62.65 + 38.57 = 179.79 ~ 180