In an isoceles triangle each of the equal sides is 10 meters and the base is 16
meters. Find the vertex angle accurate to the nearest minute. 



Draw an altitude to the base. This altitude is also a median, as well
as an angle bisector.  So it splits the base into two 8-inch parts, as
weel as bisects the vertex angle:



Just look at the laft half of the triangle.  It is a right triangle:



sin(A) =  =  = 

A = 53°8'

Therefore the entire vertex angle is twice that value:



Vertex angle = 106°16'

Edwin