Question

nathan is in a hot air balloon that has just taken off and is now floating 6.4 meters above its launching point. kaylee is standing on the ground, 6.1 meters away from the launching point. how far apart are nathan and kaylee? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Identify the right triangle

The vertical distance (height of balloon) is \( 6.4 \) m, horizontal distance (Kaylee from launch) is \( 6.1 \) m. They form a right triangle, so use Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( a = 6.4 \), \( b = 6.1 \).

Step2: Calculate \( a^2 + b^2 \)

\( 6.4^2 = 40.96 \), \( 6.1^2 = 37.21 \). Sum: \( 40.96 + 37.21 = 78.17 \).

Step3: Take the square root

\( c = \sqrt{78.17} \approx 8.8 \) (rounded to nearest tenth).

Answer:

\( 8.8 \)