Question

If the length of ZT is 4.8 units, what is the length of OT? Show all your calculations and unit measurements.

Answer 1

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.