SOLUTION: Find the missing side and angles of triangle ABC sides: A= 12 B= 13 C= 17.69 I had to find side C. So I took A^2 + B^2 = C^2 and put in 12^2 + 13^2 = C^2. 144+169=c^2.

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Question 755371: Find the missing side and angles of triangle ABC
sides:
A= 12
B= 13
C= 17.69
I had to find side C. So I took A^2 + B^2 = C^2 and put in 12^2 + 13^2 = C^2. 144+169=c^2. I added the left side and got 313 then I used the square root on both sides and got C = 17.69
Angles:
A=
B=
C= 76 degrees
How do I find the missing angles? Is my side C correct? Thank you for the help!
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Find the missing side and angles of triangle ABC
sides:
A= 12
B= 13
C= 17.69
I had to find side C. So I took A^2 + B^2 = C^2 and put in 12^2 + 13^2 = C^2. 144+169=c^2. I added the left side and got 313 then I used the square root on both sides and got C = 17.69
Angles:
A=
B=
C= 76 degrees
How do I find the missing angles? Is my side C correct?
--------------------------------------------------------------------
You have assumed this is a right triangle by using a^2 + b^2 = c^2
But it's not, in a right triangle, the hypotenuse (c) is opposite
the right angle (C) and here it is given as 76 degrees.
:
We have to use the law of cosines, which is:
c^2 = a^2 + b^2 -2(ab)*cos(C), in this problem
a=12, b=13, Angle C = 76; we will find side c:
c^2 = 12^2 + 13^2 - 2(12*13)*cos(76)
c^2 = 144 + 169 - 2(156)*.24192
c^2 = 313-75.48
c =
c = 15.41 is side c
:
Use the law of sines to find Angle A
=
15.41*sin(A) = 12*sin(76)
sin(A) =
sin(A) .7556
A = 49.1 degrees
then
B = 180 - 76 - 49.1
B = 54.9 degrees
:
summarize
sides
a = 12
b = 13
c = 15.41
Angles
A = 49.1 degrees
B = 54.9
C = 76 degrees
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