SOLUTION: In triangle ABC, the length of the altitude to side AB is 6 inches, and the measures of angles A and B are 45 and 60 degrees, respectively. What is the area of triangle ABC? expr

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Question 145856: In triangle ABC, the length of the altitude to side AB is 6 inches, and the measures of angles A and B are 45 and 60 degrees, respectively. What is the area of triangle ABC? express as a deimal to the nearest tenth.

Answer by vleith(2517) About Me  (Show Source):
You can put this solution on YOUR website!
Drop the altitude and find point D on AC. D cuts AC into two segments.
ABD has a side of 6 and A at 45. So AD is also 6.
BDC has a side 6 with C at 60. So DC is 6 / tan(60) = 3.46
AC = AD+DC = 6+3.46 = 9.46
area of ABC is bh/2 = 6*9.46/2 = 28.4 in^2