Use the image to answer the 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)
To answer this question, we need to use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean theorem can be written in the form: a^2 + b^2 = c^2, where a and b are the lengths of the two perpendicular sides (also known as the legs), and c is the length of the hypotenuse.
In this case, the height, p, is one of the legs, the base, s, is the other leg, and the hypotenuse, t, is labeled as the distance between P and S.
Since the equation given in the options has p, s, and t in it, we can use trial and error to check each option and see which one matches the Pythagorean theorem equation.
Option 1: p^2 + t^2 = s^2
Option 2: p^2 + s^2 = t^2
By comparing the options to the Pythagorean theorem, we can see that Option 2, p^2 + s^2 = t^2, is the correct equation based on the right triangle information given.
Therefore, the answer is "2".
Option 2: p2+s2=t2
thanks explain bot
The correct equation based on the right triangle shown is Option 2: p2+s2=t2.
This equation represents the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (t) is equal to the sum of the squares of the other two sides (p and s).