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