Mauricio Q.
asked • 07/15/20The Pythagorean Theorem
A right cone has a slant height of 17 feet, and the diameter of the base is 30 feet. What is the height, h, of the cone? A.8ft
B.64ft
C.13ft
D.square root of 514ft
More
1 Expert Answer
Samantha R. answered • 07/15/20
Tutor
5
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Experienced Math Student Working in Education
Since we have a slant height, we can think of that as our hypotenuse, or our C value. So C=17.
Our diameter of the base is 30, which means our radius is 15, because radius+radius=diameter. So, our base or our B=15.
Plugging this into the pythagorean theorem, we have
A2+B2=C2
A2+152=172
A2+225=289
Subtract 225 from both sides to get A2 by itself
A2=289-225
A2=64
Lastly, square root both sides (since that is the opposite operation of squaring so they cancel out) to get
A= 8
I hope this helps!
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Adam M.
Pythagorean Theorem = a^2 + b^2 = c^2 The first thing I would suggest is don't let the fact that the problem describes this as a cone instead of a triangle confuse you. We can absolutely assume that the "slant" is our Hypotenuse in this example or our "c" in the Pythagorean Theorem. The Diameter of the base would mean we would just need to take 1/2 of that amount to get one of the legs of our Right Triangle or our "b". The height is the other leg of our triangle or our "a". So now that we have identified what we have and what we need, we can use the Pythagorean Theorem to solve. a^2 + 15^2 = 17^2 Step 1. Square 15 and 17 to get 225 and 289 a^2 + 225 = 289 Step 2. Subtract 225 from 289 and get 64 - 225 - 225 a^2 = 64 Step 3. The square root of 64 is 8 The height is 8 and the answer is A. One final thing you can do to proof your work is take 8^2 + 15^2 and confirm that it equals 17^2 this way without a doubt you know you did your work correctly according to the Pythagorean Theorem.07/16/20