At one show he places three mirrors: A, B and C, in a right triangular form. If the distance between A and B is 15 more than the distance between A and C, and the distance between B and C is 15 less than the distance between A and C. What is the distance between mirror A and mirror C?

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