Hello,
I'm not sure how to go about this question.
To get to work on the first day, Jose has the following directions.
Travel 15 miles due East.
Turn right and travel 12 miles due south.
Turn right again and travel 10 miles due West.
If Jose could travel in a straight line from his house to work, how many miles would he travel?
You end up with a right triangle with the two legs being 12 miles and 5 miles.
Use the Pythagorean theorem, with c representing the hypotenuse.
a^2 + b^2 = c^2
12^2 + 5^2 = c^2
144 + 25 = c^2
169 = c^2
13 = c
Ok, thanks. But how did you get 12 and 5?
He traveled 15 miles east and then 10 miles west.
15 - 10 = 5
He traveled 12 miles south.
That gives us a triangle.
He started at point A. Went to point B, and then to point C. He ended at point D. You need to find the distance betwen point A and point D.
B_______<___15____<______A (start)
|
v
|
12
|
v
|___>____10__>___D
C
To solve this question, we need to visualize Jose's movements and calculate the distance he travels.
First, let's draw a diagram to represent his movements:
```
| W |
| ------> |
10| |
| |
| |
---------- ----------
| |
| |
12| |
| E |
| |
```
Note: E represents East, W represents West, and the arrows indicate the direction of Jose's movements.
Now, we need to calculate the distances for each leg of his journey:
Leg 1: Traveling 15 miles due East.
Leg 2: Turning right (South) and traveling 12 miles due South.
Leg 3: Turning right (West) and traveling 10 miles due West.
To calculate the total distance traveled, we can use the Pythagorean theorem, which 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, we can consider the three legs as three sides of a right triangle, with the distance traveled as the hypotenuse.
Using the Pythagorean theorem, the distance traveled would be:
Square root of [(15 + 10)^2 + 12^2]
Simplifying and calculating:
Square root of [25^2 + 12^2]
Square root of [625 + 144]
Square root of 769
The square root of 769 is approximately:
27.75
Therefore, if Jose could travel in a straight line from his house to work, he would travel approximately 27.75 miles.