SOLUTION: In triangle ABC, (bsinC)(bcosC + ccos B) = 42. Compute the area of the triangle.

Algebra ->  Trigonometry-basics -> SOLUTION: In triangle ABC, (bsinC)(bcosC + ccos B) = 42. Compute the area of the triangle.       Log On


   



Question 1176725: In triangle ABC, (bsinC)(bcosC + ccos B) = 42. Compute the area of the triangle.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

D = projection of A on +BC.
Then:
b%2Asin%28C%29+=+AD+=+h...height of the triangle ABC with respect to base BC
b%2Acos%28C%29+=+DC+(projection of side b+=+AC onto base BC)
c%2Acos%28B%29+=+BD+(projection of side c+=+AB onto base BC)
Thus
+b%2Acos%28C%29%2Bc%2Acos%28B%29+=+BD+%2B+DC+=+BC => base
So

Therefore ABC+=+42%2F2+=+21 square units