Nathan and Julia are walking along lines that form a 38 degree angle. If Nathan walks at 3.6 miles per hour and Julia walks at 4.1 miles per hour, how far apart will they be after 2 hours?
Use law of cosines:
c^2=a^2 +b^2 -2abcosC
C=38deg
a=3.6*2
b=4.1*2
Thank you Bob, your awesome :D
To find the distance between Nathan and Julia after 2 hours, we need to determine the distances each of them walked.
We can use the formula: distance = speed × time.
Let's calculate the distances separately.
Nathan's distance = Nathan's speed × time
= 3.6 miles/hour × 2 hours
= 7.2 miles.
Julia's distance = Julia's speed × time
= 4.1 miles/hour × 2 hours
= 8.2 miles.
Now, we need to find the vertical distance between Nathan and Julia after 2 hours, using the angle between the lines they are walking along.
Since the lines form a 38-degree angle, we can use the formula: vertical distance = distance × sin(angle).
Vertical distance = 7.2 miles × sin(38 degrees)
= 7.2 miles × 0.6157
≈ 4.433 miles. (rounded to three decimal places)
Therefore, after 2 hours, Nathan and Julia will be approximately 4.433 miles apart.