Mathematics

Mathematics

Problem

In △PQR, right-angled at R, the lengths PR = 9 cm and QR = 12 cm are given. Identify the trigonometric ratio you would use to calculate ∠P and briefly state why this ratio is appropriate.
Intuitive explanation

The key is recognizing which sides you know relative to angle PP. Since RR is the right angle, side QR=12QR = 12 cm is opposite to angle PP, while PR=9PR = 9 cm is adjacent to it. The tangent ratio directly relates opposite to adjacent sides, making tan⁡P=QRPR=129\tan P = \frac{QR}{PR} = \frac{12}{9} the most straightforward choice—no need to find the hypotenuse first.

Intuitive explanation

The key is recognizing which sides you know relative to angle PP. Since RR is the right angle, side QR=12QR = 12 cm is opposite to angle PP, while PR=9PR = 9 cm is adjacent to it. The tangent ratio directly relates opposite to adjacent sides, making tan⁡P=QRPR=129\tan P = \frac{QR}{PR} = \frac{12}{9} the most straightforward choice—no need to find the hypotenuse first.

Browse the problem library