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

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) (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

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

Angle B = 180 - ABD

Therefore measure of angle B is 143.13 degrees.

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