# 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:

$B=\frac{18{0}^{\circ }}{\pi }\cdot \mathrm{arcsin}\left(v\mathrm{/}b\right)=\frac{18{0}^{\circ }}{\pi }\cdot \mathrm{arcsin}\left(12\mathrm{/}13\right)=67.380{1}^{\circ }=6{7}^{\circ }2{2}^{\mathrm{\prime }}49\mathrm{"}$
$C=180-B=180-67.3801=112.619{9}^{\circ }=11{2}^{\circ }3{7}^{\mathrm{\prime }}11\mathrm{"}$

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