In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of Sin P, Cos P and tan P

Question

In &#x394; PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of Sin P, Cos P and tan P

Philoid · Accepted Answer

Given that, PR + QR = 25

PQ = 5

Let PR be x

Therefore,

QR = 25 - x

Applying Pythagoras theorem in ΔPQR, we obtain

PR² = PQ² + QR²

x² = (5)² + (25 - x)²

x² = 25 + 625 + x² - 50x

50x = 650

x = 13

Therefore,

PR = 13 cm

QR = (25 - 13) cm = 12 cm

Sin P =

Cos P =

Tan P =