Question

find the length of ad given: angle abc -60° angle dbc= 45° bc =40cm​

Answer 1

Answer:

• In Triangle DBC :

$:\implies\sf \tan(\theta)=\dfrac{Perpendicular}{Base}\\\\\\:\implies\sf \tan(45)=\dfrac{DC}{BC}\\\\\\:\implies\sf 1 =\dfrac{DC}{40}\\\\\\:\implies\sf 40 = DC\qquad...eq\:(I)$

⠀

• In Triangle ABC :

$:\implies\sf \tan(\theta)=\dfrac{Perpendicular}{Base}\\\\\\:\implies\sf \tan(60)=\dfrac{AC}{BC}\\\\\\:\implies\sf \sqrt{3} =\dfrac{AC}{40}\\\\\\:\implies\sf 40 \sqrt{3} = AC\\\\\\:\implies\sf40 \sqrt{3} = AD+DC\\\\{\scriptsize\qquad\bf{\dag}\:\:\texttt{Putting value of DC from eq. ( I )}}\\\\:\implies\sf 40 \sqrt{3} =AD+40\\\\\\:\implies\sf 40 \sqrt{3} - 40 = AD\\\\\\:\implies\sf 40( \sqrt{3} - 1) = AD\\\\\\:\implies\underline{\boxed{\sf AD = 40( \sqrt{3} - 1)\:cm}}$