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:

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

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

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

Try another example