Question

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

• A. $\frac{12}{13}$
• B. $\frac{15}{12}$
• C. $\frac{5}{12}$
• D. $\frac{5}{13}$

Answer 1

The correct option is A

$\frac{12}{13}$

Applying Pythagoras Theorem

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

⇒ $(25-QR{)}^2$ = $5^2$ + $Q{R}^2$
i.e.,$(QR-25{)}^2$ = $5^2$ + $Q{R}^2$
⇒ $Q{R}^2-50QR+625=25+Q{R}^2$

⇒ $50QR=600$

⇒ $QR=12cm$

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

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