A jogger goes 1.5km and then turns north. If the jogger finishes 1.7km from the starting point, how far north did the jogger go?
"A jogger goes 1.5km"
what was the initial direction?
Assuming he went west, we would have
n^2 + 1.5^2 = 1.7^2
n^2 = 1.7^2 - 1.5^2 = .64
n = √.64 = .8
Adjust my solution once you have fixed your typo.
To find out how far north the jogger went, we can use the Pythagorean theorem.
Let's assume the distance the jogger went north is 'x' km.
According to the problem, after going 1.5 km, the jogger finished 1.7 km from the starting point.
Using the Pythagorean theorem, we can write an equation:
(1.5)^2 + x^2 = (1.7)^2
Expanding this equation, we get:
2.25 + x^2 = 2.89
Now, subtracting 2.25 from both sides gives us:
x^2 = 2.89 - 2.25
x^2 = 0.64
Taking the square root of both sides, we get:
x = √0.64
x ≈ 0.8
Therefore, the jogger went approximately 0.8 km north.
To determine how far north the jogger went, we can use the Pythagorean theorem. Let's break down the problem step by step:
1. The jogger initially goes 1.5km, which we can consider as the distance traveled on the x-axis (east-west direction).
2. After turning north, the jogger finishes 1.7km from the starting point. We can consider this as the hypotenuse of a right triangle.
3. To find the distance traveled north (y-axis), we need to determine the length of the leg of the right triangle.
Now, let's calculate the distance traveled north:
1. Use the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the legs of the right triangle, and c is the hypotenuse.
2. Rearranging the formula: b^2 = c^2 - a^2.
3. Plug in the values: a = 1.5km and c = 1.7km.
b^2 = (1.7km)^2 - (1.5km)^2
= 2.89km^2 - 2.25km^2
= 0.64km^2.
4. Take the square root of both sides to find b:
b = sqrt(0.64km^2)
= 0.8km.
Therefore, the jogger went 0.8km north.