Question 142607: To find the hypotenuse of a right triangle the equation is a2+b2=c2, but what is the equation for finding the hypotenuse of an obtuse triangle.
Example would be a 12 foot addition to a house with a new roof having an 18 degree angle laid upon an existing roof having a 45 degree angle.
Answer by jojo14344(1513)   (Show Source):
You can put this solution on YOUR website! First, there's no hypotenuse to an obtuse triangle. There's the longest side(and I think this the one you're looking for) opposite the greatest angle(>90deg).
Let's try to picture first your problem so we can solve it better.
I'll try to explain it clearly in writing.
The existing foundation has an acute angle of 45deg, name it angle ABC. So it has a line from A to B and B to C, and the angle is on B which is 45deg, right?
Now, you added 12 ft to a new roof having 18 deg., and this became a triangle now, right? So we need to close that acute angle to make it a triangle, and that line you added will be from C to A, and we'll assign it "b"=12ft. Why "b"? Because it's opposite angle B right? Also, you have angle A as 18 deg as it was stated in the problem. Having known that we can compute for angle C:
By law, all included angles in a triangle equals 180deg.
A+B+C=180
18+45+C=180
C=180-63
C=117deg (the largest angle)
Can you pricture the triangle now? I guess so. We have to assign opposite angle A as "a" side, and opp. angle C as "c" side - and this the one you're looking for.You need 2 laws in trigo to solve this.
First we need to solve for side "a" and we use Sine Law,
a/sinA = b/sinB
a/sin18 = 12/sin45
a= 5.24ft
Next, we need to use Cosine Law for the side you're looking for, side c (longest side),
c^2 = a^2 + b^2 - 2abcosC
=(5.24)^2 + (12)^2 - 2(5.24)(12)cos117
c=sq rt[171.46 -(- 57.09)]
c=15.12 ft
Thank you,
Jojo
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