Consider a triangle ABC with
angle C = α, 0<α<π/2
AC = 17
BC = 19
AB = c
Find the number of integral values of c.
(The correct answer is 33)
angle C = α, 0<α<π/2
AC = 17
BC = 19
AB = c
Find the number of integral values of c.
(The correct answer is 33)
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I don't agree with the answer of 33 if the top limit for alpha is pi/2.
Assume that 0 is not an acceptable value for c (because it then wouldn't be a true triangle) and so start with c = 1. The maximum value of c is the integer below the value which would make alpha = pi/2 or 90 degrees.
By Pythagoras rule this occurs when
c^2 = 17^2 + 19^2 = 650 ----> c = 25 because 25^2 = 625 but 26^2 = 676.
Integer values of c are from 1 to 25.
P.S. If alpha is allowed to go up to 180 degrees then the maximum value for
c = 17 + 19 - 1 = 35
so that wouldn't give 33 either.
Assume that 0 is not an acceptable value for c (because it then wouldn't be a true triangle) and so start with c = 1. The maximum value of c is the integer below the value which would make alpha = pi/2 or 90 degrees.
By Pythagoras rule this occurs when
c^2 = 17^2 + 19^2 = 650 ----> c = 25 because 25^2 = 625 but 26^2 = 676.
Integer values of c are from 1 to 25.
P.S. If alpha is allowed to go up to 180 degrees then the maximum value for
c = 17 + 19 - 1 = 35
so that wouldn't give 33 either.
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how to get 23 as correct answer....
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