Question

In $△$ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the value of cos R.

• A. 12/13
• B. 5/13
• C. 5/12
• D. 15/12

Answer 1

The correct option is A

12/13

Applying Pythagoras Theorem

$P{R}^2$ = $P{Q}^2$ + $Q{R}^2$

$\Rightarrow$ $(QR-25{)}^2$ = $5^2$ + $Q{R}^2$

$\Rightarrow$ $Q{R}^2-50QR+625=25+Q{R}^2$

$\Rightarrow$ $50QR=600$

$\Rightarrow$ $QR=12cm$

Therefore, $PR=25-12=13cm$

So ,cos R = $\frac{QR}{PR}=\frac{12}{13}$