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Problem of the Week

Problem E

Roads All Around

Tima owns a triangular parcel of land that is created by three intersecting roads, as shown. Two of the roads meet at a right angle and two of the roads intersect at a \(25^{\circ}\) angle. If the perimeter of the triangular parcel of land is 1000 m, what is its area to the nearest 100 m\(^2\)?

Triangle A B C is enclosed by the three roads. The angle at C is twenty five degrees and at B is ninety degrees.

Recall: For any acute angle, \(\theta\), of any right-angled triangle, we define the following:

sin \(\theta= \frac{\mbox{opp}}{\mbox{hyp}}\), cos \(\theta= \frac{\mbox{adj}}{\mbox{hyp}}\), tan \(\theta= \frac{\mbox{opp}}{\mbox{adj}}\)