Answer:
6 cm
Explanation:
The triangle formed by the slant height, the height, and the radius is a right triangle with one leg 4.5 cm and hypotenuse 7.5 cm. These dimensions are in the ratio ...
4.5 : 7.5 = 3 : 5
so suggests that the dimensions are similar to those of a 3-4-5 right triangle with a scale factor of 1.5 cm.
That is, the height of the cone will be 1.5 cm · 4 = 6 cm.
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Comment on 3-4-5 right triangle
Triangles with dimensions of these ratios often show up in algebra problems because they work out nicely, avoiding irrational numbers. It is easy enough to show that a triangle with legs 3 and 4 will have a hypotenuse of 5, according to the Pythagorean theorem:
5^2 = 3^2 + 4^2
25 = 9 + 16 . . . . . . true