# Diagonals

Rhombus has two diagonals e=14 dm and f=11 dm.

Calculate the side angle and height of the rhombus.

Result

a =  8.9 dm
α =  76.31 °
h =  8.65 dm

#### Solution:

$a^2 = \left(\dfrac{e}{2}\right)^2 + \left(\dfrac{f}{2} \right)^2 \ \\ a = \sqrt{ (14/2)^2 +(11/2)^2} = 8.9 \ \text{ dm }$
\tan \dfrac{\alpha}{2} = \dfrac{f}{e} \ \\ \alpha = 2 \arctan \dfrac{f}{e} = 2 \arctan \dfrac{ 11}{ 14} = 76.31 \text{ ^\circ } = 76^\circ 18'52"
$\sin \alpha = \dfrac{ h }{ a } \ \\ h = a \sin \alpha = 8.65 \ \text{ dm }$

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