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)

Answer 1

In a right-angled triangle, the Pythagorean theorem states that the sum of the squares of the two legs (the height and the base, in this case) equals the square of the hypotenuse.

In this case:

• The height \( S T \) is \( p \).
• The base \( T P \) is \( s \).
• The hypotenuse \( P S \) is \( t \).

According to the Pythagorean theorem, we have:

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

Thus, the correct option is Option 2.

So, the answer is: 2.