Find the diagonal $d_{2}$ of a rhombus if side $a = 10 cm$ and angle $α = 6 0^{o}$ .

Answer

$33.4607 cm$

Explanation

STEP 1: find angle $β$

To find angle $β$ use formula:

α + β = 9 0^{o}

After substituting $α = 6 0^{o}$ we have:

6 0^{o} + β = 9 0^{o}

β = 9 0^{o} - 6 0^{o}

β = 3 0^{o}

STEP 2: find height $h$

To find height $h$ use formula:

sin (α) = \frac{h}{a}

After substituting $α = 6 0^{o}$ and $a = 10 cm$ we have:

sin (6 0^{o}) = \frac{h}{10}

\frac{3}{2} = \frac{h}{10}

h = \frac{3}{2} \cdot 10

h = 53

STEP 3: find diagonal $d 2$

To find diagonal $d 2$ use formula:

sin (\frac{β}{2}) = \frac{h}{d _{2}}

After substituting $β = 3 0^{o}$ and $h = 53 cm$ we have:

sin (\frac{3 0 ^{o}}{2}) = \frac{h}{d _{2}}

sin (1 5^{o}) = \frac{5 3 cm}{d _{2}}

0.2588 = \frac{5 3 cm}{d _{2}}

d_{2} = \frac{5 3 cm}{0.2588}

d_{2} = 33.4607 cm

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Find the diagonal d2​ of a rhombus if side a=10cm and angle α=60o.

33.4607cm

Find the diagonal $d_{2}$ of a rhombus if side $a = 10 cm$ and angle $α = 6 0^{o}$ .

$33.4607 cm$