Question

A lizard needs to stay a safe distance from a cactus. The diameter of the cactus is 12 inches. If the lizard is 8 inches from a point of tangency, find the direct distance between the lizard and the cactus (x). If necessary, round to the hundredths place.

Answer 1

The direct distance between the lizard and the cactus is 10 inches.

Step-by-step explanation:

To find the direct distance between the lizard and the cactus, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 between the lizard and the point of tangency is one leg of the right triangle, and the radius of the cactus (half of the diameter) is the other leg. Let's call the direct distance between the lizard and the cactus x. We can set up the following equation:

x^2 = 8^2 + (12/2)^2

x^2 = 64 + 36

x^2 = 100

x = sqrt(100)

x = 10 inches

Therefore, the direct distance between the lizard and the cactus is 10 inches.

Answer 2

We will use the Pythagorean theorem:
8² + 12² = c²
64 + 144 = c²
c = √208 ≈ 14.42
14.42 - 12 = 2.42 in
The direct distance between the lizard and the cactus is 2.42 inches.