Ratio of tans

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In this resource students are given the coordinates for each vertex of a triangle, with two of the vertices being horizontal. The challenge is to determine the ratio of the tangents of two of the angles.

Each student worksheet has a different triangle, but the solutions all have something in common.

To find the solution students can use a translation vector to shift the triangle so that one of the points is at the origin. The length along the horizontal side is given and one of the other sides can be determined using Pythagoras’ theorem. The required angles can then be found by using the sine rule.

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