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Project ID:
2010015810
Source Problem:
Accepted:
0
Clonable:
1
Easy:
0
Na obrázku je pravidelný štvorboký ihlan \(ABCDV\) s hranou \(a = 10\; \mathrm{cm}\) a telesovou výškou \(v = 10\; \mathrm{cm}\).
Určte uhol \(\varphi \) medzi bočnou hranou a hranou podstavy.
\(\mathop{\mathrm{tg}}\nolimits {\varphi} = \sqrt5
\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 65^{\circ }54^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{\sqrt5}
{5}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 24^{\circ }6^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}{2} = \frac{\sqrt5}
{5}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 48^{\circ }11^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits {\varphi} = \frac{\sqrt{10}}
{2}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 57^{\circ }41^{\prime}\)