Question

Question #a69e0

Answer 1

`A~~44.2^@`
`B ~~ 95.5^@`
`C ~~ 40.3^@`

Explanation:

By convention, `a` represents the side opposite vertex `A`, `b` represents the side opposite vertex `B`, and `c` represents the side opposite vertex `C`.

The law of cosines states that `c^2 = a^2+b^2-2abcos(C)`. Note that this is true regardless of how the sides and vertices are labeled, so it is also true that

• `b^2 = a^2+c^2-2ac cos(B)`
• `a^2 = b^2+c^2-2bc cos(A)`

If we try solving for the angle, we get

• `cos(A) = (b^2+c^2-a^2)/(2bc)`
• `cos(B) = (a^2+c^2-b^2)/(2ac)`
• `cos(C) = (a^2+b^2-c^2)/(2ab)`

Thus, applying the inverse cosine function to both sides:

• `A = arccos((b^2+c^2-a^2)/(2bc))`
• `B = arccos((a^2+c^2-b^2)/(2ac))`
• `C = arccos((a^2+b^2-c^2)/(2ab))`

Substituting in the given values `a=14, b=20, c=13` into a calculator, we get our results:

• `A~~44.2^@`
• `B ~~ 95.5^@`
• `C ~~ 40.3^@`