A spotlight is attached to the ceiling 2 feet from one wall of a room and 3 feet from the wall adjacent. How many feet is it from the intersection of the two walls?

a. 4
b. 5
c. 3 square root of 2
d. square root of 13
e. 2 square root of 3

if you can picture this, it forms a rt triangle with the shortest leg 2, the longer leg 3, and you are looking for the hypotenuse.

So, h^2 = 2^2 + 3^3
h^2 = 4 + 9
h^2 = 13
h = sqrt 13

Thank you!

you're welcome

Well, to find the distance from the spotlight to the intersection of the two walls, we can use the good old Pythagorean theorem. Let's call the distance from the spotlight to the intersection "x," since we don't know it yet.

So, we have a right triangle, where the two sides adjacent to the right angle are 2 feet and 3 feet. According to the Pythagorean theorem, the square of the length of the hypotenuse (x in this case) is equal to the sum of the squares of the other two sides.

In mathematical terms, this looks like:

x^2 = 2^2 + 3^2

Simplifying that, we get:

x^2 = 4 + 9
x^2 = 13

Now, taking the square root of both sides, we find:

x = √13

So, the distance from the spotlight to the intersection of the two walls is the square root of 13. Dang, that's irrational!

So, in the spirit of irrational numbers, let's go with option D: the square root of 13. Trust me, this answer is absolutely irrational... in a mathematical sense!

To find the distance from the spotlight to the intersection of the two walls, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right 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 two sides of the triangle are the distances from the spotlight to each of the walls.

Let's label the distance from the spotlight to the intersection of the two walls as x. We can then label the distance from the spotlight to the wall it is 2 feet away from as 2 and the distance from the spotlight to the adjacent wall as 3.

Using the Pythagorean theorem, we have:
x^2 = 2^2 + 3^2
x^2 = 4 + 9
x^2 = 13

Taking the square root of both sides, we find:
x = √13

Therefore, the distance from the spotlight to the intersection of the two walls is √13 feet.

So, the answer is option d. square root of 13.