Question

hey answer my question...........

A rhombus of side 20 cm has two angles 60° each. So find the length of the diagonals.

Answer 1

Given the length of the first diagonal  = 20cm.

(1) Shorter Diagonal(d1):

$= \ \textgreater \ \sqrt{a^2 + b^2 - 2abcos(60)}$

$= \ \textgreater \ \sqrt{(20)^2 + (20)^2 - 2(20)(20) * \frac{1}{2} }$

$= \ \textgreater \ \sqrt{400 + 400 - 800 * \frac{1}{2} }$

$= \ \textgreater \ \sqrt{800 - 400}$

$= \ \textgreater \ \sqrt{400}$

$= \ \textgreater \ 20$


(2) Longer Diagonal(d2):

$= \ \textgreater \ \sqrt{(a)^2 + (b)^2 - 2abcos(120)}$

$= \ \textgreater \ \sqrt{(20)^2 + (20)^2 - 2 * 20 * 20(- \frac{1}{2}) }$

$= \ \textgreater \ \sqrt{400 + 400 - 800 * \frac{-1}{2} }$

$= \ \textgreater \ \sqrt{400 + 400 + 400}$

$= \ \textgreater \ \sqrt{1200}$

$= \ \textgreater \ 20 \sqrt{3}$



Therefore the length of the diagonals are: $20, 20 \sqrt{3}$


Hope this helps!