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=ac=3621=15 m Δx,b,d  b2=x2+d22xdcosA  A=180πarccos(x2+d2b22 x d)=180πarccos(152+1621422 15 16)53.576453.576533435"a=36 \ \text{m} \ \\ c=21 \ \text{m} \ \\ b=14 \ \text{m} \ \\ d=16 \ \text{m} \ \\ \ \\ x=a-c=36-21=15 \ \text{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 \doteq 53.576 ^\circ \doteq 53^\circ 34'35"
B=180πarccos(x2+b2d22 x b)=180πarccos(152+1421622 15 14)66.867666.86866523"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 \doteq 66.868 ^\circ \doteq 66^\circ 52'3"
C=180B=18066.8676=113.132=113.132=113755"C=180 - B=180 - 66.8676=113.132=113.132 ^\circ =113^\circ 7'55"
D=180A=18053.5764=126.424=126.424=1262526"D=180 - A=180 - 53.5764=126.424=126.424 ^\circ =126^\circ 25'26"

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