Answer :
Driving north then east or west is 90 degrees rotation internally. Distance of Chad from his home to his final location is Option B: 130 mi
The Pythagoras theorem:
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
What is a right angled triangle?
A right angled triangle is a triangle having one of its angle with measure of 90 degrees.
The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.
Referring to the diagram attached below, as Chad moved from north driving to east driving, thus, he made a 90 degrees angle internally as perpendiculars are with 90 degrees. Then joining his first and final position, we get a right angled triangle. Thus,
Distance of Chad from final point to his home = length of AC = |AC|
- Measuring length of AB:
A is the starting point of Chad. His speed was 60 mph for the first travel in the north direction. He traveled 2 hours. Since each hour he travels 60 miles(from his speed), and he spent 2 hours so 60 + 60 = 120 miles covered.
Thus, |AB| = distance traveled in north direction is 120 miles.
- Measuring length of BC:
Similarly, as he traveled in east for 1 hour with speed 50 mph, thus, he traveled 50 miles. Thus,
Length of BC = |BC| = 50 miles.
His distance from his home A to his final position C is calculated as follows.
Using Pythagoras theorem, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{120^2 + 50^2} = \sqrt{16900} = 130 \: \rm miles\\\\[/tex]
(we took positive root since |AC| is length's measure., which is a non-negative quantity)
Thus,
Distance of Chad from his home to his final location is Option B: 130 mi
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
