Rectangular trapezoid

In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.

Correct result:

v =  12 cm
B =  67.3801 °
C =  112.6199 °

Solution:

a=12 cm b=13 cm c=7 cm  x=a−c=12−7=5 cm  v=b2−x2=132−52 cm=12 cm
B=180∘π⋅arcsin⁡(v/b)=180∘π⋅arcsin⁡(12/13)=67.3801∘=67∘22′49"
C=180−B=180−67.3801=112.6199∘=112∘37′11"

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