Students have fun and are engaged solving this right triangle trig puzzle. They solve for the lenghths of the sidesof each right triangle using the tangent ratio. Students are given the tangent ratio in lowest terms, they then find the lengths of the legs of each right triangle. After all triangle lengths are solved, they find the length and width of the rectangle.
An extension is to find the hypotenuse, cosine, and sine of each triangle. These are NOT Pythagorean triples. The length of the hypotenuse in some of the triangles is the square root of a prime number.
Students may also find the total number of rectangels in the figure,along with finding their length and width.