Question

Three sides of a triangle measure 10m, 12m, and 18m. Find the largest angle of the triangle to the nearest degree.

Answer 1

Answer:

  109°

Step-by-step explanation:

The Law of Cosines is good for finding angles when you know three sides. It tells you ...

  a^2 = b^2 + c^2 -2bc·cos(A)

where a, b, c are the side lengths and A, B, C are the opposite angles. Here, we want a=18, since the longest side is opposite the largest angle.

Solving for cos(A), we get ...

  (b^2 +c^2 -a^2)/(2bc) = cos(A)

  A = arccos((b^2 +c^2 -a^2)/(2bc)) = arccos((10^2 +12^2 -18^2)/(2·10·12))

  = arccos(-80/240) = arccos(-1/3) ≈ 109.471°

The largest angle of the triangle is about 109°.