In a triangle, the degree measure of one angle is 60 more than that of anohter. The ratio of the lengths of the sides opposite these two angles is 2:1. Fidn the degree-measure of the largest angle of this triangle.
+128407 Let the meaure of the smaller angle = A
And the measure of the other known angle be A+ 60
And by the Law of Sines
sin (A + 60) 2
_________ = ___ so we have
sin A 1
sinAcos60 + sin60cosA
___________________ = 2
sin A
sinA + √3cosA
_____________ = 2
2sin A
sinA (√3/2) cot A = 2
______ +
2sinA
(1/2) + (√3/2)cot A = 2
(√3/2)cotA = 3/2
cot A = 3 / √3
cot A = √3
arccot(√3) = A = 30°
So the second known angle = A + 60 = 90°.....and this must be the measure of the largest angle in the triangle
