# 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 =  67.38 °
C =  112.62 °

#### Solution:

$a=12 \ \text{cm} \ \\ b=13 \ \text{cm} \ \\ c=7 \ \text{cm} \ \\ \ \\ x=a-c=12-7=5 \ \text{cm} \ \\ \ \\ v=\sqrt{ b^2 - x^2 }=\sqrt{ 13^2 - 5^2 }=12 \ \text{cm}$
$B=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(v/b)=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(12/13)=67.38 ^\circ =67^\circ 22'49"$
$C=180-B=180-67.3801=\dfrac{ 5631 }{ 50 }=112.62 ^\circ =112^\circ 37'12"$

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