Find the angle $α$ of a rhombus if side $a = 14.12 cm$ and diagonal $d_{2} = 11 cm$ .

Answer

$50.038 3^{o}$

Explanation

STEP 1: find diagonal $d 1$

To find diagonal $d 1$ use formula:

d_{1}^{2} + d_{2}^{2} = 4 \cdot a^{2}

After substituting $d_{2} = 11 cm$ and $a = 14.12 cm$ we have:

d_{1}^{2} + (11 cm)^{2} = 4 \cdot (14.12 cm)^{2}

d_{1}^{2} + 121 cm^{2} == 797.4976 cm^{2}

d_{1}^{2} == 797.4976 cm^{2} - 121 cm^{2}

d_{1}^{2} = 676.4976 cm^{2}

d_{1} = 676.4976 cm^{2}

d_{1} = 26.0096 cm

STEP 2: find angle $α$

To find angle $α$ use formula:

sin (\frac{α}{2}) = \frac{d _{2}}{d _{1}}

After substituting $d_{2} = 11 cm$ and $d_{1} = 26.0096 cm$ we have:

sin (\frac{α}{2}) = \frac{11 cm}{26.0096 cm}

sin (\frac{α}{2}) = 0.4229

\frac{α}{2} = arcsin (0.4229)

\frac{α}{2} = 25.019 2^{o}

α = 25.019 2^{o} \cdot 2

α = 50.038 3^{o}

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Find the angle α of a rhombus if side a=14.12cm and diagonal d2​=11cm.

50.0383o

Find the angle $α$ of a rhombus if side $a = 14.12 cm$ and diagonal $d_{2} = 11 cm$ .

$50.038 3^{o}$