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.

Correct result:

A =  53.5764 °
B =  66.8676 °
C =  113.1324 °
D =  126.4236 °

Solution:

$$\begin{gathered} a=36\text{ m } \\ c=21\text{ m } \\ b=14\text{ m } \\ d=16\text{ m } \\ x=a-c=36-21=15\text{ m } \\ \mathrm{\Delta }x,b,d \\ {b}^2=x^2+d^2-2xd\cos A \\ A={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arccos ({\displaystyle \frac{x^2+d^2-b^2}{2\cdot x\cdot d}})={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arccos ({\displaystyle \frac{15^2+16^2-14^2}{2\cdot 15\cdot 16}})=53.5764^{\circ }=53^{\circ }34^{\mathrm{\prime }}35\mathrm{"} \end{gathered}$$

$B={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arccos ({\displaystyle \frac{x^2+b^2-d^2}{2\cdot x\cdot b}})={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arccos ({\displaystyle \frac{15^2+14^2-16^2}{2\cdot 15\cdot 14}})=66.8676^{\circ }=66^{\circ }52^{\mathrm{\prime }}3\mathrm{"}$

$C=180-B=180-66.8676=113.1324^{\circ }=113^{\circ }{7}^{\mathrm{\prime }}57\mathrm{"}$

$D=180-A=180-53.5764=126.4236^{\circ }=126^{\circ }25^{\mathrm{\prime }}25\mathrm{"}$

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