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

Question

asked Nov 26, 2021 153k views

1 Answer

Fmorency · Answer 1 · 2021-12-01T02:26:24+0000

Answer:

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°.