Question
two sides of a triangle is 10 and 12 what is the third angle
Answers
GPT-4o mini
To find the third angle of a triangle when two sides are given (10 and 12), we need to know either the length of the third side or one of the angles opposite to the given sides. However, you can find the angles of the triangle using the Law of Cosines if you have the length of the third side, or the Law of Sines if you know at least one angle.
If we denote the sides as \(a = 10\), \(b = 12\), and \(c\) is the unknown length of the third side, the angles opposite to sides \(a\), \(b\), and \(c\) can be denoted as \(A\), \(B\), and \(C\) respectively.
The Law of Cosines states:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
You can also find angles if you know one angle and the lengths of the opposite sides using the Law of Sines:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Please provide either the length of the third side or one of the angles, and I can help you find the third angle of the triangle.
If we denote the sides as \(a = 10\), \(b = 12\), and \(c\) is the unknown length of the third side, the angles opposite to sides \(a\), \(b\), and \(c\) can be denoted as \(A\), \(B\), and \(C\) respectively.
The Law of Cosines states:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
You can also find angles if you know one angle and the lengths of the opposite sides using the Law of Sines:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Please provide either the length of the third side or one of the angles, and I can help you find the third angle of the triangle.