Rectangular trapezoid

In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.

Correct answer:

v =  12 cm
B =  67.3801 °
C =  112.6199 °

Step-by-step explanation:

$$\begin{gathered} a=12\text{ cm } \\ b=13\text{ cm } \\ c=7\text{ cm } \\ x=a-c=12-7=5\text{ cm } \\ v=\sqrt{b^2-x^2}=\sqrt{13^2-5^2}\text{ cm}=12\text{ cm} \end{gathered}$$

$B={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arcsin (v\mathrm{/}b)={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arcsin (12\mathrm{/}13)=67.3801^{\circ }=67^{\circ }22^{\mathrm{\prime }}49\mathrm{"}$

$C=180-B=180-67.3801=112.6199^{\circ }=112^{\circ }37^{\mathrm{\prime }}11\mathrm{"}$

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