Question

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

Answer 1

Answer:

The smallest angle of the triangle is 33.030°.

Step-by-step 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°:

$\cos A = -\frac{6^{2}-9^{2}-11^{2}}{2\cdot (9)\cdot (11)}$

$\cos A = 0.838$

$A \approx 33.030^{\circ}$

$\cos B = -\frac{9^{2}-6^{2}-11^{2}}{2\cdot (6)\cdot (11)}$

$\cos B = 0.575$

$B \approx 54.847^{\circ}$

$C = 180^{\circ} - A - B$

$C = 180^{\circ} - 33.030^{\circ} - 54.847^{\circ}$

$C = 92.123^{\circ}$

The smallest angle of the triangle is 33.030°.