law of cosines
m<c=60, a=12,b=15 triangle
The law of cosines is:
a^2 = b^2 + c^2 - 2cosA
or
b^2 = a^2 + c^2 - 2cosB
or
c^2 = a^2 + b^2 - 2cosC
the lower case letters are sides, the capital letters are for angles. For this problem, you would do
c^2 = 12^2 + 15^2 - 2cos60
That gives you side c. After that, you should be able to use the law of sines to find the other two angles of the triangle.
The Law of Cosines is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is commonly used to solve triangles when we have information about the lengths of the sides and/or the measures of the angles.
In your case, you have a triangle with side lengths a = 12, b = 15, and the angle opposite side c is m<c = 60 degrees. To determine the length of side c, you can use the Law of Cosines.
The formula for the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(m<c)
To solve for side c, substitute the given values into the equation:
c^2 = 12^2 + 15^2 - 2(12)(15) * cos(60)
c^2 = 144 + 225 - 2(12)(15) * 0.5 (since cosine of 60 degrees is 0.5)
c^2 = 369 - 2(12)(15) * 0.5
c^2 = 369 - 360
c^2 = 9
Taking the square root of both sides, we get:
c = √9 = 3
So, the length of side c in the given triangle is 3 units.