SOLUTION: Alright, this is kind of hard to explain, but I'll try to do my best. I have a triangle. It's slanted. The side to the far left (looks kind of like a base) is side x. across fro

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Question 386773: Alright, this is kind of hard to explain, but I'll try to do my best.
I have a triangle. It's slanted. The side to the far left (looks kind of like a base) is side x. across from the "base" there's a segment, used so that it splits the ttriangle into one smaller triangle and one smallish quadrilateral. The length of this segment is 8. The top of the quadrilateral is y, the bottom is 4. The top part of the smaller triangle is 5, and the bottom part is 7.
I'm supposed to find x and y. I've attempted calling it a midsegment, however the segment does not bisect anything. I can't use the pythagorean theory because I can't tell if it's a 90 degree angle or not.
Please help!
Thanks so much,
Katie
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
It's slanted. The side to the far left (looks kind of like a base) is side x. across from the "base" there's a segment, used so that it splits the triangle into one smaller triangle and one smallish quadrilateral. The length of this segment is 8. The top of the quadrilateral is y, the bottom is 4. The top part of the smaller triangle is 5, and the bottom part is 7.
:
If I understand this rightly, the small triangle sides are 8, 5, 7
If this is the case you can find the top angle (opposite the segment) using the law of cosines
a^2 = b^2 + c^2 - 2bc*cos(A)
using the small triangle values
8^2 + 5^2 + 7^2 - 2(5*7)*cos(A)
64 = 74 - 70*cos(A)
70cos(A) = 74 - 64
cos(A) =
A = 81.8 degrees
:
Now is the segment parallel to x, it would help to know that?
If it is you can find y:
=
:
Then use the law cosines again to find x