A convex quadrilateral has area 30 and side lengths 5, 6, 9 and 7, in that order. Denote by θ the measure of the acute angle formed by the diagonals of the quadrilateral. Then tan θ can be written in the form m/n, where m and n are relatively prime positive integers. Find m+n.

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.