Question

In $△PQR$, right-angled at $Q,PR+QR=25$ cm and $PQ=5$ cm. Determine the values of $\sin P,\cos P$ and $\tan P$.

Answer 1

A] PR+QR = 25

PR = 25 - QR

using Pythagoras theorem,

$(5{)}^2+Q{R}^2=P{R}^2$

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

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

$\therefore QR=12$

PR = 25 - QR = 13

$sinP=\frac{12}{13}$ $cosP=\frac{5}{13}$ $tanP=\frac{12}{5}$