# A light is placed 5 m from the center of a giant globe 3 m in diameter, what will be the length of the wire?

## To find the length of the wire, we'll use the Pythagorean theorem.

Step 1: Draw a diagram to represent the situation. Let's draw a triangle where the light is at one vertex, the center of the globe is at another vertex, and the wire is the hypotenuse of the triangle.

Step 2: In the triangle, the radius of the globe is given as half its diameter, which is 3 m. Therefore, the radius is 3 m/2 = 1.5 m.

Step 3: We can now label the sides of the triangle. The side adjacent to the light is the distance from the light to the center of the globe, which is given as 5 m. The side opposite to the light is the radius of the globe, which we found to be 1.5 m.

Step 4: Now, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

According to the theorem, we have:

(hypotenuse)^2 = (adjacent side)^2 + (opposite side)^2

Let's plug in the values we know:

(hypotenuse)^2 = (5 m)^2 + (1.5 m)^2

(hypotenuse)^2 = 25 m^2 + 2.25 m^2

(hypotenuse)^2 = 27.25 m^2

Step 5: To find the length of the wire (hypotenuse), we need to take the square root of both sides:

hypotenuse = √(27.25 m^2)

hypotenuse ≈ 5.22 m

Therefore, the length of the wire is approximately 5.22 meters.

## To find the length of the wire, we need to calculate the distance from the light to any point on the circumference of the giant globe.

First, let's visualize this situation. We have a light source at a point outside the globe, and we want to find the distance from that point to the globe's circumference.

Now, let's break it down step by step:

Step 1: Find the radius of the giant globe
The diameter of the globe is given as 3 m. The radius is half the diameter, so the radius formula is:
radius = diameter / 2 = 3 m / 2 = 1.5 m

Step 2: Calculate the distance from the light source to the center of the globe.
The distance from the light source to the center of the globe is given as 5 m.

Step 3: Apply the Pythagorean theorem.
Now, we can use the Pythagorean theorem to find the distance from the light source to any point on the circumference of the globe. The Pythagorean theorem states that in a right-angled 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 distance from the light source to the center of the globe is the hypotenuse, and the radius of the globe is one of the other sides.

Let's call the distance we want to find 'x'. We have:
x^2 = 5^2 - 1.5^2
x^2 = 25 - 2.25
x^2 = 22.75

Step 4: Solve for 'x'.
To find the length of the wire, 'x', we need to extract the square root of 22.75. So,
x = sqrt(22.75)
x ≈ 4.769 m

Therefore, the length of the wire is approximately 4.769 meters.