Answer:
60
Step-by-step explanation:
We have the following sides:
AB, AC, BC
By means of the statement we know that:
The distance between A and B is 15 more than the distance between A and C, that is:
AB = AC + 15
The distance between B and C is 15 less than the distance between A and C
BC = AC - 15
We can infer that the longest side is AB, therefore being right triangular form, we have to:
AC ^ 2 + BC ^ 2 = AB ^ 2
Replacing we have:
AC ^ 2 = AB ^ 2 - BC ^ 2
AC ^ 2 = (AC + 15) ^ 2 - (AC - 15) ^ 2
AC ^ 2 = (AC ^ 2 + 30 * AC + 225) - (AC ^ 2- 30 * AC + 225)
AC ^ 2 = 60 * AC
AC = 60
Which means that the distance between mirror A and C is 60.
To check, we have:
AB = (60 ^ 2 + 45 ^ 2) ^ (1/2) = (5625) ^ (1/2) = 75
AB = AC + 15 = 60 + 15 = 75
