Question

in the given right triangle, find the side labeled x. x =

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is hypotenuse, \( a,b \) are legs. Here, hypotenuse \( c = 2 \), one leg \( a = 1 \), another leg \( b = x \). So \( 1^2 + x^2 = 2^2 \).

Step2: Solve for \( x \)

Simplify: \( 1 + x^2 = 4 \). Subtract 1: \( x^2 = 3 \). Take square root: \( x = \sqrt{3} \) (since length positive).

Answer:

\(\sqrt{3}\)