Question
In a right triangle, if the altitude drawn to the
hypotenuse divides the triangle into two triangles of equal area, what is the value of the smallest angle?Solution
Let the right triangle be ABC with ∠ C = 90°. Let the altitude from C to AB divide the triangle into two equal-area triangles. The area of the triangle is (1/2) * base * height. Since the two smaller triangles have equal area, the altitude divides the hypotenuse into two equal parts. Thus, triangle ABC is an isosceles right triangle, and the smallest angle is 45°.
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