Triangle tan product and sum

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In this resource the side lengths of a triangle are given. The challenge is to find the ratio of the product of each of the tangents, divided by the sum of each of the tangents.

Each student worksheet contains a different triangle, but the answers all have something in common.

The solution involves repeated use of the cosine rule, together with work on surds and fractions. The answer is that the ratio is equal to 1 in each case.

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