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Project ID:
2010015808
Source Problem:
Accepted:
0
Clonable:
1
Easy:
1
Na obrázku je pravidelný štvorboký ihlan so štvorcovou podstavou s hranou \(a = 6\; \mathrm{cm}\) a telesovou výškou \(v = 10\; \mathrm{cm}\).
Určte uhol \(\varphi \).
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{10}
{3\sqrt2}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 67^{\circ }\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{10}
{3}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 73^{\circ }18^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}{2} = \frac{3\sqrt2}
{10}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 45^{\circ }59^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi}2 = \frac{3}
{10}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 33^{\circ }24^{\prime}\)