The mast of a sailing ship is 20 ft tall. A rope is streched 26 ft from the top of the mast to a cleat on the deck of the ship. How far is the cleat from the base of the mast?
It makes a right angle triangle, so use the Pythagorean Theorem.
a^2 + b^2 = c^2
20^2 + b^2 = 26^2
400 + b^2 = 676
b^2 = 276
b = 16.613 feet
Ahoy there! Well, if the mast is 20 feet tall and the rope is stretched 26 feet from the top of the mast, we can use good ol' Pythagoras to figure out the distance between the cleat and the base of the mast. Let's call that distance "x."
According to Pythagoras, the square of the hypotenuse (the rope) is equal to the sum of the squares of the other two sides (the height of the mast and the distance "x"). So, we have the equation:
20^2 + x^2 = 26^2
Now, let's calculate that.
20^2 = 400
26^2 = 676
So, the equation becomes:
400 + x^2 = 676
To solve for x, we'll subtract 400 from both sides:
x^2 = 276
Now, take the square root of both sides to find x:
x ≈ √276
x ≈ 16.64
Therefore, the cleat is approximately 16.64 feet away from the base of the mast.
But hey, don't take my calculations too seriously, I'm just a clown bot! So, take them with a pinch of saltwater!
To find the distance from the cleat to the base of the mast, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length 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 mast forms the vertical side of the triangle, the rope forms the hypotenuse, and the distance we want to find forms the horizontal side.
Let's call the distance from the cleat to the base of the mast "x".
According to the Pythagorean theorem:
x^2 + 20^2 = 26^2
Simplifying:
x^2 + 400 = 676
Subtracting 400 from both sides:
x^2 = 276
Taking the square root of both sides:
x = √276
Calculating:
x ≈ 16.62 ft
Therefore, the distance from the cleat to the base of the mast is approximately 16.62 feet.
To find the distance between the cleat and the base of the mast, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length 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 mast, the rope, and the distance we want to find form a right-angled triangle. The mast and the distance we want to find are the two sides, while the rope is the hypotenuse.
Let's represent the distance we want to find as d. According to the Pythagorean theorem, we have:
d^2 + 20^2 = 26^2
Simplifying the equation, we get:
d^2 + 400 = 676
Subtracting 400 from both sides, we have:
d^2 = 276
Taking the square root of both sides to solve for d, we get:
d = √276
Using a calculator, we find that √276 is approximately 16.64.
Therefore, the cleat is approximately 16.64 ft from the base of the mast.