Respuesta :
Answer:
[tex]\partial \theta = 0.003[/tex]
Explanation:
we know that
[tex]sin\theta = \frac{3.8}{146.4}[/tex]
[tex]\theta = sin^{-1} \frac{3.8}{146.4}[/tex]
[tex]\theta = 1.484°[/tex]
[tex]\theta = 1.484° *\frac{\pi}{180} = 0.0259 radians[/tex]
as we see that [tex]sin\theta = \theta[/tex]
relative error[tex] \frac{\partial \theta}{\theta} = \frac{\partial X}{X_1} +\frac{\partial X}{X_2}[/tex]
Where X_1 IS HEIGHT OF ROCK
[tex]X_2[/tex] IS THE HEIGHT OF ROAD
[tex]\partial X[/tex] = uncertainity in measuring distance
[tex]\partial X = 0.05[/tex]
Putting all value to get uncertainity in angle
[tex]\frac{\partial \theta}{0.0259} = \frac{0.05}{3.8} +\frac{0.05}{146.4}[/tex]
solving for [tex]\partial \theta[/tex] we get
[tex]\partial \theta = 0.003[/tex]
