When don is in the middle of the lake swimming towards the south shore, Dawn jumps in from the north shore and swims after him. When Don is 10 yards from the south shore,Dawn is 5 yards behind him and 60 yards from the north shore.The distance from the north shore to the south shore is ___ Yards?
Please help me
Don is 10 yards from the south shore and Dawn is 5 yards behind him, implies that Dawn is 15 yards from the south shore. Also at that time, Dawn is 60 yards from the north shore, so clearly the north shore and south shore are 75 yards apart
To find the distance from the north shore to the south shore, we can create a triangle using Don, Dawn, and the north and south shores.
Let's call the distance from the north shore to the south shore "x" yards.
From the given information, we know that when Don is 10 yards from the south shore, Dawn is 5 yards behind him and 60 yards from the north shore.
This forms a right-angled triangle. The distance from the north shore to Dawn and the distance from Dawn to Don form the two legs of the triangle, and the distance from the north shore to the south shore is the hypotenuse.
Using the Pythagorean theorem, we can solve for x:
x^2 = (60^2) + (5^2)
x^2 = 3600 + 25
x^2 = 3625
x = √3625
x ≈ 60.20
Therefore, the distance from the north shore to the south shore is approximately 60.20 yards.
To find the distance from the north shore to the south shore, we can create a diagram and use the Pythagorean theorem.
Let's assume that the distance from the north shore to the south shore is represented by the variable "x" yards.
From the given information, we know that when Don is 10 yards from the south shore, Dawn is 5 yards behind him and 60 yards from the north shore.
Now, if we draw a line from Don's position to the south shore, we create a right triangle. The vertical side of the triangle represents Don's distance from the south shore (10 yards), the horizontal side represents the distance from the north shore to Dawn's position (x - 60 yards), and the hypotenuse represents the distance from Dawn's position to the south shore (x - 5 yards).
According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.
So we have:
(10)^2 + (x - 60)^2 = (x - 5)^2
Expanding and simplifying:
100 + x^2 - 120x + 3600 = x^2 - 10x + 25
Combining like terms:
0 = 110x - 3475
Solving for x:
110x = 3475
x = 31.59
Therefore, the distance from the north shore to the south shore is approximately 31.59 yards.