Can I retrace the altitude?
As shown above, I've drawn a right triangle with a hypotenuse of 10. However, I could not figure out the altitude (as shown in the dotted lines).
Which of the following could be the altitude in question?
Select one or more
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1 solution
The locus of right angles of all possible right triangles with a given hypotenuse is a semicircle with the same diameter, since the angle inscribed in a semicircle is always a right angle. Therefore, the different altitudes of a right triangle with a hypotenuse of 1 0 will correspond with the different heights of the semicircle with a diameter of 1 0 , which would be 0 < x ≤ 5 .
This means that out of the options given, 3 , 4 , and 5 are possible altitudes, but not 6 .