in abc, c=60 degrees,a=12, and b=5. find c.
We usually use Uppercase letters to represent angles, and lowercase for side lengths.
I resume the question as follows:
in abc, =60°,a=12, and b=5. find c.
We can solve this using the cosine rule:
c²=a²+b²-2abcos(C)
Substitute the numbers and take the square-root of c² to get c.
Use law of cosines:
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 12^2 + 5^2 - 2 * 12 * 5 * cos(60°)
c^2 = 144 + 25 - 120*cos(60°)
c^2 = 169 - 120 * 0.5
c^2 = 169 - 60 = 109
c = sqrt(109) = 10.4403
To find the missing angle, c, in a triangle ABC, where a = 12, b = 5, and c = 60 degrees, we can use the Law of Cosines.
The Law of Cosines states that in a triangle with sides a, b, c, and angle C opposite side c, the following relationship holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we know:
c^2 = 12^2 + 5^2 - 2 * 12 * 5 * cos(60)
Now, let's solve for c. First, calculate the value inside the cosine function:
cos(60) = 0.5 (you can refer to a cosine table or calculate it using a calculator).
Now, substitute the values back into the equation:
c^2 = 12^2 + 5^2 - 2 * 12 * 5 * 0.5
c^2 = 144 + 25 - 120
c^2 = 49
To find c, take the square root of both sides:
c = sqrt(49)
c = 7
Therefore, in triangle ABC, when c = 60 degrees, a = 12, and b = 5, the value of c is 7.