# Children playground

The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.

Result

A =  53.576 °
B =  66.868 °
C =  113.132 °
D =  126.424 °

#### Solution:

$a = 36 \ m \ \\ c = 21 \ m \ \\ b = 14 \ m \ \\ d = 16 \ m \ \\ \ \\ x = a-c = 36-21 = 15 \ m \ \\ \Delta x,b,d \ \\ \ \\ b^2 = x^2+d^2 - 2xd \cos A \ \\ \ \\ A = \dfrac{ 180^\circ }{ \pi } \cdot \arccos( \dfrac{ x^2+d^2-b^2 }{ 2 \cdot \ x \cdot \ d } ) = \dfrac{ 180^\circ }{ \pi } \cdot \arccos( \dfrac{ 15^2+16^2-14^2 }{ 2 \cdot \ 15 \cdot \ 16 } ) \doteq 53.5764 = 53.576 ^\circ = 53^\circ 34'35"$
$B = \dfrac{ 180^\circ }{ \pi } \cdot \arccos( \dfrac{ x^2+b^2-d^2 }{ 2 \cdot \ x \cdot \ b } ) = \dfrac{ 180^\circ }{ \pi } \cdot \arccos( \dfrac{ 15^2+14^2-16^2 }{ 2 \cdot \ 15 \cdot \ 14 } ) \doteq 66.8676 = 66.868 ^\circ = 66^\circ 52'3"$
$C = 180 - B = 180 - 66.8676 = 113.132 = 113.132 ^\circ = 113^\circ 7'55"$
$D = 180 - A = 180 - 53.5764 = 126.424 = 126.424 ^\circ = 126^\circ 25'26"$

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