An isosceles triangle whose equal sides form an angle θ and whose third side has length t sits on top of a square with sides of length w as in the diagram. Assuming the base of the triangle is parallel to the side of the square, what value of w makes the intersection of the square and triangle have the largest area?

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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.