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WAEC Mathematics 2010 Paper

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Question : 49

Total: 49

In the diagram, < WOX = 60^o, < YOE = 50^o and < OXY = 30^o. What is the bearing of x from y?

300^o
240^o
190^o
150^o

Solution:

Concept:

The bearing of

X

from

Y

is measured clockwise from the north direction at

Y

. Use the straight line

WOE

and the angle sum of

\triangle OXY

.

Explanation:

From the diagram,

W

,

O

and

E

lie on a straight line.

So

\angle XOE = 180^\circ - \angle WOX = 180^\circ - 60^\circ = 120^\circ

.

Given

\angle YOE = 50^\circ

,

\angle XOY = \angle XOE - \angle YOE = 120^\circ - 50^\circ = 70^\circ

.

In

\triangle OXY

,

\angle OXY = 30^\circ

.

Hence

\angle OYX = 180^\circ - 70^\circ - 30^\circ = 80^\circ

.

At

Y

, the ray

YO

makes

50^\circ

with the west direction.

So the ray

YX

is

80^\circ - 50^\circ = 30^\circ

north of west.

West has bearing

270^\circ

, so the bearing of

X

from

Y

is

270^\circ + 30^\circ = 300^\circ

.

Answer:

300^\circ

(Option A).

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