Question

. A lizard needs to stay a safe distance from a cactus. The diameter of the cactus is 14 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.. . A.. x = 3.63 in.. B.. x = 4.57 in.. C.. x = 7.26 in.. D.. x = 17.63 in..

Answer 1

We will use Pythagorean theorem:
x - The direct distance between the lizard and the cactus;
r = 7 - radius of the cactus;
x + 7 - the distance between the lizard and the center of the cactus:
( x + 7 )² = 7²  + 8²
( x + 7)² = 49 + 64
( x + 7 )² = 113
x + 7 = √ 113 
x + 7 = 10.63
x = 10.63 - 7
x = 3.63
Answer: A)  

Answer 2

Using the equation:
8^2 = x(x+14)
64=x^2 +14x
x^2 +14x-64=0
using quadratic formula :
we get 2 values:
3.63 and -17.63
negative is not possible so our answer is 3.63