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".
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".
Answers
GPT-4o mini
The correct equation based on the properties of a right-angled triangle formed by the height \( S T \), the base \( T P \), and the hypotenuse \( P S \) is given by the Pythagorean theorem, which states that in a right triangle:
\[
\text{(Height)}^2 + \text{(Base)}^2 = \text{(Hypotenuse)}^2
\]
In terms of your labels, this can be expressed as:
\[
p^2 + s^2 = t^2
\]
This corresponds to Option 2.
Thus, the answer is: **"2"**.
\[
\text{(Height)}^2 + \text{(Base)}^2 = \text{(Hypotenuse)}^2
\]
In terms of your labels, this can be expressed as:
\[
p^2 + s^2 = t^2
\]
This corresponds to Option 2.
Thus, the answer is: **"2"**.