Right triangle trigonometrics

Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)

Correct result:

a =  17.3205 cm
C =  90 °

Solution:

$$\begin{gathered} b=10\text{ cm } \\ c=20\text{ cm } \\ a=\sqrt{c^2-b^2}=\sqrt{20^2-10^2}=10\sqrt{3}\text{ cm}=17.3205\text{ cm} \end{gathered}$$

$C=180-(60+30)=90^{\circ }$

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