Question

to get from home to his friend amandas house, bobby would have to walk 4.9 miles due north. to get from home to his friend gretas house, bobby would have to walk 1.3 miles due east. what is the straight-line distance between amandas house and gretas house? if necessary, round to the nearest tenth. miles

Explanation:

Step1: Identify the triangle type

The paths from home to Amanda (north) and home to Greta (east) are perpendicular, forming a right triangle. Let \( a = 4.9 \) (north), \( b = 1.3 \) (east), and \( c \) be the straight - line distance (hypotenuse).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle, \( c=\sqrt{a^{2}+b^{2}} \). Substitute \( a = 4.9 \) and \( b = 1.3 \) into the formula:
First, calculate \( a^{2}=(4.9)^{2}=24.01 \) and \( b^{2}=(1.3)^{2}=1.69 \).
Then, \( a^{2}+b^{2}=24.01 + 1.69=25.7 \).
Finally, \( c=\sqrt{25.7}\approx5.1 \) (rounded to the nearest tenth).

Answer:

\( 5.1 \)