Children playground

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

Correct answer:

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

Step-by-step explanation:

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

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

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

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

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