Pyramid

Pyramid has a base a = 3cm and height in v = 15 cm.

a) calculate angle between plane ABV and base plane
b) calculate angle between opposite side edges.

Correct answer:

α =  84.29 °
β =  11.36 °

Step-by-step explanation:

$$\begin{gathered} a=3cm \\ v=15cm \\ \tan \alpha =\frac{v}{a/2}=\frac{15}{3/2} \\ \alpha =\arctan \frac{15}{3/2}=84.29^{\circ }=84°17^{\prime }22" \end{gathered}$$

$$\begin{gathered} \tan \beta /2=\frac{a}{\sqrt{v^2+(a/2{)}^2}} \\ \beta =2\arctan \frac{a}{\sqrt{v^2+(a/2{)}^2}} \\ \beta =2\arctan 0.0995 \\ \beta =11.36^{\circ }=11°21^{\prime }54" \end{gathered}$$

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