The parallel sides of a trapezium have lenghts 5cm and 8cm..The other two sides have the lenghts 6cm and 4cm..Find the angles of the trapezium?

Answer 1

If AB=8 and DC=5, then if the altitude is h,

h = 4sinA = 6sinB

h cotA + 5 + h cotB = 8
4 sinA cotA + 5 + 6 sinB cotB = 8
4cosA + 5 + 6cosB = 8
4cosA + 6cosB = 3

solve for A and B.

Note that D = (90-A)+90 = 180-A
and similarly for C.