Question

Use the geometric mean to find the missing measure. If necessary, round the answer to the nearest tenth. Pythagorean Theorem: $g = √a^2 + b^2$

a) $g = √a ⋅ b$
b) $g = √a^2 - b^2$
c) $g = √a^2 + b^22$
d) $g = √2ab$

Answer 1

The correct formula to use for the geometric mean in context of the Pythagorean theorem for a right triangle is g = √(a² + b²), where g is the length of the hypotenuse and a and b are the lengths of the other two sides.

Step-by-step explanation:

The question involves finding the correct formula for the geometric mean in the context of the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

This theorem can be expressed as the equation a² + b² = c². To find the length of the hypotenuse given the lengths of the other two sides, you can rearrange the equation to solve for c: c = √(a² + b²). Therefore, the correct formula to use for finding the missing measure, g, when you are given the lengths of the sides of a right triangle is g = √(a² + b²).