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Two hikers come to a ravine and want to know how wide it is. They set up two similar triangles as shown in the diagram. How far is it across the ravine?

Two hikers come to a ravine and want to know how wide it is They set up two similar triangles as shown in the diagram How far is it across the ravine class=

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Answer:

d = 80 ft

Step-by-step explanation:

Start with angle BCA, tan(BCA) = 30/15 so BCA = 63.43 degrees.

BCA = ECD since they are opposite angles.

tan ECD = d/40

40 tan(63.4degrees) = d

d = 80 ft

Alternatively, you can use similar triangles since the angles are the same, BCA = ECD, CED = CAB, and CBA = EDC. In that case use proportions to get 30/15 = d/40 so 2 = d/40 and d = 80.