Find plane's acceleration from mass on a string

[psal]

Homework Statement

A pendulum has a length L = 1.13m. It hangs straight down in a jet plane about to take off as shown by the dotted line in the figure. The jet then accelerates uniformly, and while the plane is accelerating, the equilibrium position of the pendulum shifts to the position shown by the solid line, with D = 0.370m. Calculate the magnitude of the plane's acceleration.

Homework Equations

Lsinθ = D
a = gsinθ

The Attempt at a Solution

sinθ = 0.37/1.13
θ = 19.11 deg
9.8sin(19.11) = 3.209

I thought that is the correct way to solve it, but I am not getting the correct answer, and I cannot think of another way to go about it.

 

[azizlwl]

I think it is called fictitous force.
You assume there is a force pulling it to the right.

 

[nasu]

Or write Newton's second law for horizontal and vertical directions.

By the way, one can tell that you result is not right without going through the calculations. If it were, you will have a horizontal string (angle=90 degrees) when a=g. There will be no tension component to balance the weight.

 

[psal]

Okay, did I at least calculate the angle correctly?

Edit: Figured it out. Thanks for the help.