Find the angle $α$ of a rhombus if side $a = 12 cm$ and diagonal $d_{1} = 18 cm$ .

Answer

$123.74 9^{o}$

Explanation

STEP 1: find diagonal $d 2$

To find diagonal $d 2$ use formula:

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

After substituting $d_{1} = 18 cm$ and $a = 12 cm$ we have:

(18 cm)^{2} + d_{2}^{2} = 4 \cdot (12 cm)^{2}

324 cm^{2} + d_{2}^{2} = 576 cm^{2}

d_{2}^{2} = 576 cm^{2} - 324 cm^{2}

d_{2}^{2} = 252 cm^{2}

d_{2} = 252 cm^{2}

d_{2} = 67 cm

STEP 2: find angle $α$

To find angle $α$ use formula:

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

After substituting $d_{2} = 67 cm$ and $d_{1} = 18 cm$ we have:

sin (\frac{α}{2}) = \frac{6 7 cm}{18 cm}

sin (\frac{α}{2}) = \frac{7}{3}

\frac{α}{2} = arcsin (\frac{7}{3})

\frac{α}{2} = 61.874 5^{o}

α = 61.874 5^{o} \cdot 2

α = 123.74 9^{o}

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Find the angle α of a rhombus if side a=12cm and diagonal d1​=18cm.

123.749o

Find the angle $α$ of a rhombus if side $a = 12 cm$ and diagonal $d_{1} = 18 cm$ .

$123.74 9^{o}$