Question

find the unknown side of the triangle when x = 10 m and y = 11 m.
image of a right triangle with legs x and unknown, hypotenuse y
part 1 of 4
the length of the hypotenuse, c, is 11 ✔️ 11 m. if we call the other known side a we know that a = 10 m.
we will use the pythagorean theorem to find the unknown side, b.
part 2 of 4
substitute 10 for a and 11 for c into the equation given by the pythagorean theorem and simplify the squares.
( a^2 + b^2 = c^2 )
( square^2 + b^2 = 11^2 )
( square + b^2 = 121 )

Explanation:

Step1: Substitute \( a = 10 \) into \( a^2 \)

We know \( a = 10 \), so substitute it into \( a^2 \). Then \( 10^2 = 100 \). So the first blank is \( 10 \) and the second blank is \( 100 \) because \( 10^2 = 100 \).

Step2: Verify the substitution

After substituting \( a = 10 \) and \( c = 11 \) into the Pythagorean theorem \( a^2 + b^2 = c^2 \), we get \( 10^2 + b^2 = 11^2 \), which simplifies to \( 100 + b^2 = 121 \).

Answer:

First blank: \( 10 \), Second blank: \( 100 \)