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Example Question #353 : Geometry
The largest angle of an obtuse isosceles triangle has a measure of . If the length of the two equivalent sides is , what is the length of the hypotenuse?
The height of the obtuse isosceles triangle bisects the angle and forms two congruent right triangles. The hypotenuse of each of these triangles is either side of equivalent length, and we can see that the base of either triangle makes up half of the hypotenuse of the obtuse isosceles triangle. Because we know the angle opposite each base is half of , or , we can use the sine of this angle to find the length of the base. As there are two congruent right triangles that make up the obtuse isosceles triangle, the length of either base makes up half of the overall hypotenuse, so we then multiply the result by to obtain the final answer. In the following solution, is the length of the base of one of the right triangles, is the length of the two equivalent sides, and is the length of the hypotenuse: