SOLUTION: In triangle ABC, angle B is an obtuse angle, AB=15, BC=20, and the area of the triangle is 90. What is the measure of angle B? thank you

Algebra ->  Triangles -> SOLUTION: In triangle ABC, angle B is an obtuse angle, AB=15, BC=20, and the area of the triangle is 90. What is the measure of angle B? thank you      Log On


   

Question 473019: In triangle ABC, angle B is an obtuse angle, AB=15, BC=20, and the area of the triangle is 90. What is the measure of angle B?
thank you
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Area = (1/2)*base*height
Let BC be the base of the triangle, Area is 90, h is height
90+=+%281%2F2%29%2A20%2Ah
90+=+10h
9+=+h
Now imagine a perpendicular line drawn straight down from A, call it point D
Then ADB makes a right triangle, where the hypotenuse is AB and one leg is h.
Now find angle ABD which is the supplement to angle B.
Using trig relationship: Sin = opp/hyp
sin%28ABD%29=+9%2F15
ABD+=+sin%5E-1%289%2F15%29+=+36.87
Angle B = 180 - ABD
B+=+180+-+36.87+=+143.13
Therefore measure of angle B is 143.13 degrees.