Find the length of the diagonal AB: (5 points)

Question

You would first use ? on the bottom of the box rectangle to find the diagonal CB = ?
Then use CB as ? of the triangle ACB, with AB being the ?. AB is approximately = ?

answer options: a leg, square root 7,89 cm, 13 cm, hypotenuse, area of a rectangle, 3 cm, Pythagorean theorem, 5 cm, perimeter of a rectangle, and 73 cm.

Answer 1

To find the length of the diagonal AB, we first need to find the length of the diagonal CB using the Pythagorean theorem.

Let the sides of the rectangle be 3 cm and 4 cm.

Using the Pythagorean theorem: CB^2 = 3^2 + 4^2
CB^2 = 9 + 16
CB^2 = 25
CB = √25
CB = 5 cm

Now, CB becomes the hypotenuse of right triangle ACB, with AC and AB being the legs.

Using the Pythagorean theorem again: AB^2 = AC^2 + CB^2
AB^2 = 3^2 + 5^2
AB^2 = 9 + 25
AB^2 = 34
AB ≈ √34
AB ≈ 5.83 cm

Therefore, the length of the diagonal AB is approximately 5.83 cm.

Answer 2

If you knew that the slant height of the cone = 13 cm, and the radius of the cone = 5 cm, how would you find the height of the cone? (4 points)
Step 1: ?
Step 2: ?
Step 3: ?
Step 4: ?

Answer options: set up the equation 5^2 + h^2 = 13^2, Square 5 and 13 to get 25 +h^2 = 169, subtract 25 from both sides to get h^2 = 144, and take the square root of both sides h = 12 cm.

Answer 3

To find the height of the cone, you would follow these steps:

Step 1: Set up the equation using the Pythagorean theorem, where the radius is 5 cm and the slant height is 13 cm: 5^2 + h^2 = 13^2
Step 2: Square 5 and 13 to get 25 + h^2 = 169
Step 3: Subtract 25 from both sides to get h^2 = 144
Step 4: Take the square root of both sides to find the height: h = 12 cm

Therefore, the height of the cone is 12 cm.