Question

question 1 points 2
martha climbs 40 steps to reach the first floor of a building. if the vertical and horizontal distance of each step is 1.5 ft and 1 ft, find the distance between the start and end points of each step.

○ 1 ft

○ 1.5 ft

○ 1.8 ft

○ 40 ft

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the vertical and horizontal distances of a step are the two legs, and we need to find the hypotenuse (distance between start and end points of the step).

Step2: Recall the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(c = \sqrt{a^2 + b^2}\).

Step3: Assign values to \(a\) and \(b\)

Here, the vertical distance \(a = 1.5\) ft and the horizontal distance \(b = 1\) ft.

Step4: Calculate the hypotenuse

Substitute \(a = 1.5\) and \(b = 1\) into the formula:

$$ c = \sqrt{(1.5)^2 + (1)^2} = \sqrt{2.25 + 1} = \sqrt{3.25} \approx 1.8 \text{ ft} $$

Answer:

1.8 ft (corresponding to the option with "1.8 ft")