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Question

A rock and a sunflower are on the same side of a ravine and are 125 m apart. A birch tree is on the

opposite side of the ravine. The angle formed between the line joining the rock and the sunflower and the

line joining the rock and the birch tree is 25°. The angle formed by the line joining the rock and the

sunflower and the line joining the sunflower and the birch tree is 72°. What is the width of the ravine?

Answer 1

Let R represent the vertex of the 25 degree angle, S represent the vertex of the 72 degree angle, and B represent the vertex of the remaining angle. The lines joining the rock, sunflower, and birch tree create a triangle (RBS). Two angles are known, so the remaining angle is 180° - 72°- 25° = 83°. A line drawn from the birch tree perpendicular to the line joining the rock and sunflower (call the perpendicular intersection P) creates two right triangles and would be the width of the ravine. Using the law of sines, the length of the line joining the rock and the birch tree (line RB) can be calculated: sin 72°/RB = sin 83°/125. RB then is 119.7 m. As triangle RBP is a right triangle, Side BP (the width of the ravine) = sin 25° x 119.7m = 50.6 m.

Draw a diagram of the problem; it should make it more clear.