A triangle has two corners with angles of # pi / 4 # and # (5 pi )/ 8 #. If one side of the triangle has a length of #7 #, what is the largest possible area of the triangle?
1 Answer
Explanation:
Given two angles, the third one in a triangle is fixed. In this case it is
We now have three angles and a side, and can calculate the other sides using the Law of Sines, and then calculate the height for the area.
https://www.mathsisfun.com/algebra/trig-solving-asa-triangles.html
We now use Heron's formula for the area:
where
http://mste.illinois.edu/dildine/heron/triarea.html
https://www.mathopenref.com/heronsformula.html