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Question

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.

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
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Answer 1

For a right-angled triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (t) is equal to the sum of the squares of the lengths of the other two sides (p and s).

According to the labeling:

• p is the height (one leg of the triangle)
• s is the base (the other leg of the triangle)
• t is the hypotenuse

Thus, the correct equation according to the Pythagorean theorem would be:

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

Rearranging this gives:

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

Correspondingly, this matches Option 2. Therefore, the correct answer is:

2