SOLUTION: Select the correct answer. An equilateral triangle B uppercase A uppercase C. Side uppercase A B is of length lowercase c equals 8 and side B uppercase C is of length lowercase a

Algebra ->  Triangles -> SOLUTION: Select the correct answer. An equilateral triangle B uppercase A uppercase C. Side uppercase A B is of length lowercase c equals 8 and side B uppercase C is of length lowercase a       Log On


   



Question 1206093: Select the correct answer.
An equilateral triangle B uppercase A uppercase C. Side uppercase A B is of length lowercase c equals 8 and side B uppercase C is of length lowercase a equals 3. Angle at B is beta equals 57.53 degrees.
Which measurement of acute triangle ABC can you find by direct substitution of the labeled measures in the Law of Cosines?
A.
AC
B.
m∠
C.
m∠
D.
none


Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52893) About Me  (Show Source):
You can put this solution on YOUR website!
.

Different parts of this post do contradict each other.

As a result, this post is a full bucket of nonsense.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

An equilateral triangle has all sides+equal. Your triangle is not an equilateral triangle.

In any triangle ABC,
a%5E2+=+b%5E2+%2B+c%5E2+-+2bc%2Acos%28+A+%29
b%5E2+=+a%5E2+%2B+c%5E2+-+2ac%2Acos%28+B%29
c%5E2+=+a%5E2+%2B+b%5E2+-+2ab%2A+cos+%28C%29

given:
c=8
a=3
< B=57.53
Which measurement of acute triangle ABC can you find by direct substitution of the labeled measures in the Law of Cosines?
answer:
A.
AC (or side b)
proof:
b%5E2+=+3%5E2+%2B+8%5E2+-+2%2A3%2A8%2Acos%28+57.53%29
b%5E2+=+47.23081907263568
b=sqrt%2847.23081907263568%29
b=6.9

then you can find angles A and C
a%5E2+=+b%5E2+%2B+c%5E2+-+2bc%2Acos%28+A+%29
3%5E2+=+6.9%5E2+%2B+8%5E2+-+2%2A6.9%2A8%2Acos%28+A+%29
2%2A6.9%2A8%2Acos%28+A+%29=3%5E2+-+6.9%5E2+%2B+8%5E2+
110.4cos%28+A+%29=25.39
cos%28+A+%29=25.39%2F110.4
cos%28+A+%29=0.22998188405797101
A=cos%5E-1%280.22998188405797101%29
A=76.7°
then
C=180-%2857.53%2B76.7%29
C=45.77°