If the length of ZT is 4.8 units, what is the length of OT? Show all your calculations and unit measurements.
To solve for the length of OT, we need to use the Pythagorean theorem since OT is the hypotenuse of right triangle ZTO.
Pythagorean theorem: a^2 + b^2 = c^2
Where:
a = length of ZT = 4.8 units
b = length of TO (OT)
c = length of OT
We can rearrange the formula to solve for b:
b^2 = c^2 - a^2
b^2 = OT^2 - ZT^2
b^2 = OT^2 - 4.8^2
b^2 = OT^2 - 23.04
Since ZT and OT are perpendicular to each other, we can use the Pythagorean theorem to solve for OT:
OT^2 = ZT^2 + TO^2
OT^2 = 4.8^2 + b^2
OT^2 = 23.04 + b^2
Now, we substitute the value of b^2 from above into the equation:
OT^2 = 23.04 + OT^2 - 23.04
0 = OT^2 - OT^2
0 = 0
This means that b (or OT) can be any value since both sides of the equation are equal. So the length of OT could be any value when the length of ZT is 4.8 units.