Question

In a $△$ABC, right angled at B, AB + AC = 25 units, and BC = 5 units.
What is $\sin C$?

Answer 1

Given, AB + AC = 25 units.

Let AB = $x$, then AC = $25-x$
Apply pythagoras theorem,

$\begin{array}{cc}{\text{AC}}^2& ={\text{AB}}^2+{\text{BC}}^2\\ (25-x{)}^2& =x^2+5^2\\ 625+x^2-50x& =x^2+25\\ 625-50x& =25\\ 50x& =600\\ x& =12\end{array}$

$25-x=25-12=13$

So, AB = 12 units and AC = 13 units

$\begin{array}{cc}\sin C& =\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\ & =\frac{12}{13}\end{array}$