# Pyramid

Pyramid has a base a = 5cm and height in v = 8 cm.

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

Correct result:

α =  72.65 °
β =  33.22 °

#### Solution:

$\tan \alpha = \dfrac{v}{a/2} = \dfrac{ 8 }{ 5/2} \ \\ \alpha = \arctan \dfrac{ 8 }{ 5/2} = 72.65 ^\circ = 72^\circ 38'46"$
$\ \\ \tan \beta/2 = \dfrac{ a }{ \sqrt{v^2+(a/2)^2} } \ \\ \beta = 2 \arctan \dfrac{ a }{ \sqrt{v^2+(a/2)^2} } \ \\ \beta = 2 \arctan 0.29827 \ \\ \ \\ \beta = 33.22 ^\circ = 33^\circ 13'1"$

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