SOLUTION: How do I find the area of this triangle: {{{drawing(400,350,-1,3,-1,2.5, locate(-.8,.2,"60°"), locate(1.6,.2,"40°"),locate(.05,.81,12), triangle(-1,0,2.064177772,0,0,sqrt(3)), g

Algebra ->  Triangles -> SOLUTION: How do I find the area of this triangle: {{{drawing(400,350,-1,3,-1,2.5, locate(-.8,.2,"60°"), locate(1.6,.2,"40°"),locate(.05,.81,12), triangle(-1,0,2.064177772,0,0,sqrt(3)), g      Log On


   

Question 639217: How do I find the area of this triangle:



thank you!
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


Since the formula for the area of a triangle is

            A = 1%2F2b·h

and we have the height = h = 12, we must find the base. Let the left 
part of the base be x and the right part of the base be y.



To find x, we use TANGENT=OPPOSITE%2FADJACENT

tan(60°) = 12%2Fx

Multiply both sides by x:

x·tan(60°) = 12

Divide both sides by tan(60°)

         x = 12%2Ftan%28%2260%B0%22%29
         x = 6.9282


To find y, we also use TANGENT=OPPOSITE%2FADJACENT

tan(40°) = 12%2Fy

Multiply both sides by y:

y·tan(40°) = 12

Divide both sides by tan(40°)

         y = 12%2Ftan%28%2240%B0%22%29
         y = 14.3010

the base = b = x + y = 6.9282 + 14.3010 = 21.2292

            A = 1%2F2b·h
            A = 1%2F2(21.2292)(12)
            A = 127.3752  

Edwin