Find the angle $α$ of a rhombus if area $A = 143 cm$ and diagonal $d_{1} = 26 cm$ .

Answer

$50.05 8^{o}$

Explanation

STEP 1: find diagonal $d 2$

To find diagonal $d 2$ use formula:

A = \frac{d _{1} \cdot d _{2}}{2}

After substituting $A = 143 cm$ and $d_{1} = 26 cm$ we have:

143 cm = \frac{26 cm \cdot d _{2}}{2}

143 cm \cdot 2 = 26 cm \cdot d_{2}

286 cm = 26 cm \cdot d_{2}

d_{2} = \frac{286 cm}{26 cm}

d_{2} = 11

STEP 2: find angle $α$

To find angle $α$ use formula:

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

After substituting $d_{2} = 11 cm^{0}$ and $d_{1} = 26 cm$ we have:

sin (\frac{α}{2}) = \frac{11}{26 cm}

sin (\frac{α}{2}) = \frac{11}{26} cm^{-} 1

\frac{α}{2} = arcsin (\frac{11}{26} cm^{-} 1)

\frac{α}{2} = 25.02 9^{o}

α = 25.02 9^{o} \cdot 2

α = 50.05 8^{o}

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Find the angle α of a rhombus if area A=143cm and diagonal d1​=26cm.

50.058o

Find the angle $α$ of a rhombus if area $A = 143 cm$ and diagonal $d_{1} = 26 cm$ .

$50.05 8^{o}$