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 answer should be 6 if i am right

Answer 2

10 in

Explanation:

We are given that

Diameter of cactus=d=12 in

Radius of cactus=
`(d)/(2)=(12)/(2)=6 in`

Distance of lizard from point of tangency=8 in

We have to find the direct distance between lizard and cactus.

In triangle OAB,

OA=6 in

AB=8 in

Pythagorous theorem:
`(Hypotenuse)^2=(base)^2+(perpendicular\;side)^2`

Using pythagorous theorem

`OB^2=(6)^2+(8)^2=100`

`OB=√(100)=10 in`

Hence, the direct distance of lizard from cactus=10 in