Question 1191559: Let's say, a man has to check the schedule of the boat trips at the information center, A. The 200-m path to the information center and the 400-m path to the boat rental dock, B, intersect at the parking lot, C, forming a right angle. He walks straight from the parking lot to the lake D as shown, where a sign tells him that he is approximately 357.77 m from the dock. How far is the man from the information center? What is the equation to represent the situation? If the man will go back to the parking lot from the information center. What is total distance he walked?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Distance from the man to the information center:**
We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the sides of the right triangle are:
* The path to the information center (200 m)
* The path to the boat rental dock (400 m)
* The man's path from the parking lot to the lake (unknown)
Let's call the unknown distance "x". The equation to represent the situation is:
x² + 400² = 357.77²
Solving for x, we get:
x = √(357.77² - 400²) = 200 m
Therefore, the man is 200 meters from the information center.
**2. Total distance walked:**
If the man walks back to the parking lot from the information center, he will walk an additional 200 meters. So the total distance he walked is:
200 m (parking lot to lake) + 200 m (information center to parking lot) = 400 m
**Answer:**
The man is 200 meters from the information center. The equation to represent the situation is x² + 400² = 357.77². If the man goes back to the parking lot from the information center, the total distance he walked is 400 meters.
Answer by ikleyn(52747)  (Show Source):
You can put this solution on YOUR website! .
In the post by @PChill something is very confusing and incorrect.
He writes an equation for the right angled triangle in the form
x^2 + 400^2 = 357.77^2,
but such an equation can not have real solutions for x,
since the left side is deliberately greater than the right side.
It means that the logic of the solution is SELF-CONTRADICTORY
and can not lead to correct answer.
This " solution " is FATALLY WRONG.
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