Question

Find the measure of the smallest angle of the triangle whose sides have lengths 6,9, and 11

Answer 1

The smallest angle of the triangle is 33.030°.

Explanation:

The angles of triangle can be determined with the help of the Law of Cosine and the fact that sum of all angles equals to 180°:

`\cos A = -(6^(2)-9^(2)-11^(2))/(2\cdot (9)\cdot (11))`

`\cos A = 0.838`

`A \approx 33.030^(\circ)`

`\cos B = -(9^(2)-6^(2)-11^(2))/(2\cdot (6)\cdot (11))`

`\cos B = 0.575`

`B \approx 54.847^(\circ)`

`C = 180^(\circ) - A - B`

`C = 180^(\circ) - 33.030^(\circ) - 54.847^(\circ)`

`C = 92.123^(\circ)`

The smallest angle of the triangle is 33.030°.