Shaun rides 8 kilo meters west from his house to school. After school he rides 6 kilo meters north to Mario's house. What is the distance from Mario's house to Shaun's house measured in a straight line?
sqrt(64 + 36) = 10
(a three four five right triangle)
You are finding the hypoenuse, using the Pythagoran theorem
D^2 = 8^2 + 6^2 = 100
D = √100 = 10 km
To find the distance from Shaun's house to Mario's house measured in a straight line, we can use the Pythagorean theorem.
First, let's visualize the scenario. Suppose Shaun's house is located at point A, and Mario's house is located at point B. Shaun rides 8 kilometers west from his house to school, which means he moves 8 kilometers to the left. Then, after school, he rides 6 kilometers north, which means he moves 6 kilometers upwards.
We can draw a right-angled triangle where side AB represents the distance from Shaun's house to Mario's house measured in a straight line, side AC represents Shaun's westward movement, and side BC represents Shaun's northward movement.
Now, we can apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the other two sides (AC and BC).
In this case, AC represents the 8 kilometer westward movement, and BC represents the 6 kilometer northward movement. So, we have:
AB^2 = AC^2 + BC^2
Substituting the values:
AB^2 = 8^2 + 6^2
AB^2 = 64 + 36
AB^2 = 100
Taking the square root of both sides to solve for AB:
AB = √100
AB = 10
Therefore, the distance from Mario's house to Shaun's house measured in a straight line is 10 kilometers.