Answer:
10 in
Step-by-step explanation:
We are given that
Diameter of cactus=d=12 in
Radius of cactus=[tex]\frac{d}{2}=\frac{12}{2}=6 in[/tex]
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: [tex](Hypotenuse)^2=(base)^2+(perpendicular\;side)^2[/tex]
Using pythagorous theorem
[tex]OB^2=(6)^2+(8)^2=100[/tex]
[tex]OB=\sqrt{100}=10 in[/tex]
Hence, the direct distance of lizard from cactus=10 in
