Julia drives 10km due west of her home. then she heads 15 km south. what is the total distance that she has travelled from his house?
This question has nothing to do with trig, it is simply a Pythagorean application.
x^2= 10^2 + 15^2= 325
x = √325 = appr 18 km
To find the total distance Julia has traveled from her house, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance traveled west is 10 km and the distance traveled south is 15 km. These two distances form the legs of a right triangle, with the total distance traveled as the hypotenuse.
To find the total distance:
1. Square the distance traveled west: 10 km * 10 km = 100 km^2
2. Square the distance traveled south: 15 km * 15 km = 225 km^2
3. Add the squared distances together: 100 km^2 + 225 km^2 = 325 km^2
4. Take the square root of the sum: √325 km^2 ≈ 18.03 km
Therefore, Julia has traveled approximately 18.03 km from her house.
To find the total distance that Julia has traveled from her house, we can use the concept of a right-angled triangle.
First, let's consider Julia's journey in a coordinate plane. We'll say her house is at the origin (0,0), and she drives 10 km due west, which means she ends up at (-10,0). Then, she heads 15 km south, bringing her to (-10,-15).
To find the distance Julia has traveled, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the horizontal distance Julia traveled (10 km due west) is one side of the right triangle, and the vertical distance Julia traveled (15 km south) is the other side. The total distance traveled would then be the hypotenuse of the right triangle.
Using the Pythagorean theorem, we can calculate the distance as follows:
Distance = sqrt((horizontal distance)^2 + (vertical distance)^2)
= sqrt((-10)^2 + (-15)^2)
= sqrt(100 + 225)
= sqrt(325)
≈ 18.03 km (rounded to two decimal places)
Therefore, Julia has traveled approximately 18.03 km from her house.