Question

ABDE is a trapezium​​​​​​ with $AE\parallel BD$ and $ED\perp BD$. Also, AC is drawn parallel to the side DE.

Find the values of $\text{cot}\theta and\text{cosec}\theta$, respectively, from the figure above.

Answer 1

Consider the figure ACDE,
$AE\parallel CD$ and $AC\parallel DE$ and $AD\perp CD$

$\therefore$ ACDE is a rectangle.

CD = AE = 10 units

BC = BD - CD = 16 - 10 = 6 units

Now, in $△ABC$,

$\angle C={90}^{\circ }$

Now, from Pythagoras' theorem,

$A{C}^2+B{C}^2=A{B}^2$

$A{C}^2+6^2={10}^2$
.
$AC=\sqrt{(100-36)}=8units$

$\text{cot}\theta =\frac{AC}{BC}=\frac{8}{6}=\frac{4}{3}\text{cosec}\theta =\frac{AB}{BC}=\frac{10}{6}=\frac{5}{3}$