Round side length to the nearest tenth and angle measures to the nearest degree?
1.) a= 2 , b= 5 , c=7
Use the Law of Cosines to solve for the values of A, B, and C (which are the angles). First will solve for the variable A.
If a=2, b=5, and c=7; then substitute the values into the Law of Cosines formula which contains cos A.
Which is: a^2 = b^2 +c^2 - 2bc(cos A)
Solve the equation for cos A so that: (cos A) = (a^2 - b^2 - c^2) / (-2bc)
Now substitute: (cos A) = (2^2 - 5^2 - 7^2) / [-2(5)(7)]
Then: (cos A) = (-70) / (-70) or (cos A) = 1
To isolate A use the arccosine function which looks like this: cos^-1
So: A = cos^-1 (1)
which equals 0 degrees.
Since a triangle cannot have an angle measuring 0 degrees, the triangle does not exist.
This triangle does not exist because the sum of its two smallest sides is not greater than its longest side.