Trapezoid interior angles

The area for shooting training has the shape of a trapezoid, the parallel sides of which are 36 m, 21 m long, and the remaining sides are 14 m, 16 m long. Determine the size of the interior angles with a longer base.

Final Answer:

α =  53.5764 °
β =  66.8676 °

Step-by-step explanation:

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

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

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