SOLUTION: Determine the area of the triangle △ABC in the diagram below. Round the answer to two decimal places if needed. https://docs.google.com/document/d/1WvDRbA4pYipC9pLNNUzfvn46KWw

Algebra ->  Surface-area -> SOLUTION: Determine the area of the triangle △ABC in the diagram below. Round the answer to two decimal places if needed. https://docs.google.com/document/d/1WvDRbA4pYipC9pLNNUzfvn46KWw      Log On


   

Question 1182275: Determine the area of the triangle △ABC in the diagram below. Round the answer to two decimal places if needed.
https://docs.google.com/document/d/1WvDRbA4pYipC9pLNNUzfvn46KWwN1aCmeV3zJjlbuQM/edit?usp=sharing
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!


The bottom △BCD is isosceles, so we draw the median DE, which is also
the perpendicular bisector of the base, and also the bisector of the vertex
angle D.  So it bisects the angle into two 35o angles.



sin%28%22%22%3CBDE%29=%22BE%22%2F%22BD%22

sin%2835%5Eo%29=BE%2F15%29

Multiply both sides by 15

15sin%2835%5Eo%29=BE

8.603646545=BE

So the base of △ABC is BC which is twice that amount, so

BC=2%288.603646545%29=17.20729309

Now we need the altitude of △ABC, which is AC

tan%28%22%22%3CA%29=%22BC%22%2F%22AC%22

tan%2827%5Eo%29=17.20729309%2F%22AC%22%29

Multiply both sides by AC

%22AC%22tan%2827%5Eo%29=17.20729309%29

%22AC%22=17.20729309%2Ftan%2827%5Eo%29

%22AC%22=33.77121419

Area of △ABC = 1%2F2base%22%22%2A%22%22altitude

Area of △ABC = expr%281%2F2%29%2ABC%2AAC

Area of △ABC = expr%281%2F2%29%2A17.20729309%2A33.77121419

Area of △ABC = expr%281%2F2%29%2A17.20729309%2A33.77121419

Area of △ABC = Area+of+%E2%96%B3ABC+=+%7B%7B%7B290.5555903

Rounded to two decimal places, 290.56

Edwin