Find the angle $β$ of a rhombus if diagonal $d_{1} = 30 cm$ and diagonal $d_{2} = 16 cm$ .

Answer

$25.538 1^{o}$

Explanation

STEP 1: find angle $α$

To find angle $α$ use formula:

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

After substituting $d_{2} = 16 cm$ and $d_{1} = 30 cm$ we have:

sin (\frac{α}{2}) = \frac{16 cm}{30 cm}

sin (\frac{α}{2}) = \frac{8}{15}

\frac{α}{2} = arcsin (\frac{8}{15})

\frac{α}{2} = 32.23 1^{o}

α = 32.23 1^{o} \cdot 2

α = 64.461 9^{o}

STEP 2: find angle $β$

To find angle $β$ use formula:

α + β = 9 0^{o}

After substituting $α = 64.461 9^{o}$ we have:

64.461 9^{o} + β = 9 0^{o}

β = 9 0^{o} - 64.461 9^{o}

β = 25.538 1^{o}

This page was created using

Rhombus Calculator

About the Author

Welcome to MathPortal. This website's owner is mathematician Miloš Petrović. I designed this website and wrote all the calculators, lessons, and formulas.

If you want to contact me, probably have some questions, write me using the contact form or email me on mathhelp@mathportal.org.

Send Me A Comment

Main Navigation

Online Math Calculators

Find the angle β of a rhombus if diagonal d1​=30cm and diagonal d2​=16cm.

25.5381o

Find the angle $β$ of a rhombus if diagonal $d_{1} = 30 cm$ and diagonal $d_{2} = 16 cm$ .

$25.538 1^{o}$