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:

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

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

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