Question

If x = 9 cm and z = 15 cm, what is the length of y?

Answer 1

Given that the problem does not specify if y is opposite, adjacent or hypotenuse side, I will provide two solutions to this problem.

Case 1. Y is the hypotenuse side. (See figure 1)

According to the Pythagorean Theorem, for a right triangle, it is true that:

$c^{2}=a^{2}+b^{2}$

being c the hypotenuse side and a and b the opposite and adjacent side respectively. So, for the figure 1 it is true that:

z = a = 15cm
x = b = 9cm
y = c = ?

$y^{2}=9^{2}+15^{2}=306$
∴ $y=\sqrt{306}=17.492cm$

Case 2. Y is the opposite side (The same happens as if it were the adjacent side). (See figure 2)

From the equation:

$c^{2}=a^{2}+b^{2}$

For the figure:

y = a = ?
x = b = 9cm
z = c = 15cm

We need to isolate a, so:

$a^{2}=c^{2}-b^{2}$

$a^{2}=15^{2}-9^{2}=144$

∴ $y=a=\sqrt{144}=12cm$