A right-angled triangle has the vertices labeled upper P upper S upper T. The height upper S upper T is labeled p; the base upper T upper P is labeled s; and the hypotenuse upper P upper S is labeled t.

Question

Which equation is a true equation based on the right triangle shown?

Option 1: p2+t2=s2

Option 2: p2+s2=t2

Option 3: There is not enough information about the triangle to write an equation.

Enter "1", "2", or "3".
(1 point)
Remaining Attempts : 3

Answer 1

In a right-angled triangle, the relationship between the lengths of the sides is defined by the Pythagorean theorem, which states that the square of the length of the hypotenuse (in this case, segment PS, labeled as t) is equal to the sum of the squares of the lengths of the other two sides (the height ST, labeled as p, and the base TP, labeled as s).

This relationship can be expressed mathematically as:

\[ t^2 = p^2 + s^2 \]

Rearranging the equation gives:

\[ p^2 + s^2 = t^2 \]

This matches Option 2 perfectly.

Thus, the correct answer is:

2