Answer:
15.0 in
Explanation:
You want the height of a cone with radius 8 in and slant height 17 in.
Pythagorean theorem
The right triangle shown in the figure has height h, base x = 8 in, and slant height y = 17 in. The Pythagorean theorem tells you the relationship between these side lengths:
x² +h² = y²
8² +h² = 17²
h² = 17² -8² = 289 -64 = 225
h = √225 = 15.0
The height of the cone is 15.0 inches.
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Additional comment
A triple of 3 integers that form the sides of a right triangle is called a "Pythagorean triple." The triple in this problem is one of those: {8, 15, 17}. Other Pythagorean triples you will often see in algebra, trig, and geometry problems are {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {9, 40, 41}. You will also see multiples of these, for example 3×{3, 4, 5} = {9, 12, 15}.
It can be worthwhile to remember some of these. For this problem, recognizing 8 and 17 as part of the triple {8, 15, 17} means you can write down the answer with no further work.