Question

In a $△$ABC, right angled at B, AC - AB = 1 unit, and BC = 7 units.
What is $\text{cosec}C$?

• A. $\frac{24}{25}$
• B. $\frac{24}{7}$
• C. $\frac{7}{24}$
• D. $\frac{25}{24}$

Answer 1

The correct option is D $\frac{25}{24}$

Given,
AC - AB = 1 unit
BC = 7 units

Let AB = $x$, then AC = $x+1$
Apply pythagoras theorem,

$\begin{array}{cc}{\text{AC}}^2& ={\text{AB}}^2+{\text{BC}}^2\\ (x+1{)}^2& =x^2+7^2\\ 1+x^2+2x& =x^2+49\\ 1+2x& =49\\ 2x& =48\\ x& =24\end{array}$

$1+x=1+24=25$

So, AB = 24 units and AC = 25 units.

$\begin{array}{cc}\text{cosec}C=\frac{\text{Hypotenuse}}{\text{Perpendicular}}& \\ & =\frac{AC}{AB}\\ & =\frac{25}{24}\end{array}$