Question

In the following figure :
AD $\perp$ BC, AC $=$ 26, CD $=$ 10, BC $=$ 42, $\angle DAC$=$x$ and $\angle B$=$y$.
Find the value of :If $\cot x=\frac{m}{10}$.Find $m$

Answer 1

Given: $△ABC$, $AD\perp BC$, $AC=26$, $CD=10$, $BC=42$
Now, In $△ACD$,
$A{C}^2=C{D}^2+A{D}^2$
${26}^2={10}^2+A{D}^2$
$A{D}^2=576$
$AD=24$
Now, $\cot x=\frac{B}{P}=\frac{AD}{CD}=\frac{24}{10}=2.4$