Question

The sides of a triangle are in the ratio 2 : 3 : 4. Find the cosine of the largest angle of this triangle.

Answer 1

- .25

Explanation:

We can just say the sidelengths are 2 3 and 4. This IS NOT a right traingle ( you can check with Pythagorean Theorem)

The largest angle will have the largest opposite side = 4

Using the Law of Cosines

4^2 = 2^2 + 3^2 - 2 (2)(3) cos (largest angle)

solving this for cos (largest angle) = -.25 ( which relates to 104.5°)