1 Answer

Alejandro Quiroz · Answer 1 · 2023-05-11T05:15:13+0000

We will work at first with the small triangle ADC

$m\angle DAC+m\angle C=m\angle ADB$

mm
$m\angle DAC=55-20=35^(\circ)$ We will use the sine rule

$(65)/(\sin35)=(AD)/(\sin 20)$

By using the cross multiplication

$\begin{gathered} AD*\sin 35=65*\sin 20 \\ AD=(65\sin 20)/(\sin 35) \end{gathered}$

In triangle ABD

We will use

$\sin 55=(x)/(AD)$

Then

$x=AD\sin 55$

Substitute AD by its value above

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