Question

You have a rod with a length of 146.4 cm. You prop up one end on a brick which is 3.8 cm thick. Your uncertainty in measuring these distances is ±0.05 cm. What is the angle that the rod makes with the table?

_______ degrees
What is the uncertainty in that angle?
________ degrees

Answer 1

`\partial \theta = 0.003`

Step-by-step explanation:

we know that

`sin\theta = (3.8)/(146.4)`

`\theta = sin^(-1) (3.8)/(146.4)`

`\theta = 1.484°`

`\theta = 1.484° *(\pi)/(180) = 0.0259 radians`

as we see that
`sin\theta = \theta`

relative error
`(\partial \theta)/(\theta) = (\partial X)/(X_1) +(\partial X)/(X_2)`

Where X_1 IS HEIGHT OF ROCK

`X_2` IS THE HEIGHT OF ROAD

`\partial X` = uncertainity in measuring distance

`\partial X = 0.05`

Putting all value to get uncertainity in angle

`(\partial \theta)/(0.0259) = (0.05)/(3.8) +(0.05)/(146.4)`

solving for
`\partial \theta` we get

`\partial \theta = 0.003`