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WAEC Mathematics 2025 Paper

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Question : 45

Total: 50

The bearing of two points Q and R from a point P are 030º and 120º, respectively. If | PQ | = 12 m and | PR | = 5 m, find the distance QR.

11 m
13 m
9 m
7 m

Solution:

Concept:

The angle between the two bearings gives

\angle QPR

, and the triangle is right-angled at

P

.

Explanation:

The bearing of

Q

from

P

is

030^\circ

.

The bearing of

R

from

P

is

120^\circ

.

So,

\angle QPR = 120^\circ - 030^\circ = 90^\circ

.

Thus,

\triangle PQR

is right-angled at

P

.

Using Pythagoras theorem:

QR^2 = PQ^2 + PR^2

QR^2 = 12^2 + 5^2 = 144 + 25 = 169

QR = \sqrt{169} = 13 \text{ m}

Answer:

13

m (Option B).

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