Help with trigonometry.

[KFS]

In Example 1: I don't understand the procedure of this exercise. I do know why the derivative of the angle with respect to time is 2π/30. What I don't understand is the rest. It says x=10tanθ, how is this possible? It gives me, and the computer, by tanθ=opposite/adjacent, x=10/tanθ, not 10tanθ. What I don't understand either is why both derivatives (dx/dθ) and (dθ/dt) are multiplying. Why is x=8 choosen? Why not any other number?

Thanks for the help.

[Ghideon]

5 hours ago, KFS said:

Why is x=8 choosen? Why not any other number?

It looks like the problem could have been based on other number but author picked x=8.

5 hours ago, KFS said:

It gives me, and the computer, by tanθ=opposite/adjacent, x=10/tanθ, not 10tanθ.

Isn't θ is the angle at the lighthouse L between lines LQ and LP? Then x=8 is the opposite and 10 is the adjacent.
tanθ=opposite/adjacent or tanθ=x/10 so x=10tanθ

Hint regarding the derivatives: are you familiar with the chain rule for computing the derivative of the composition of two (or more) functions?

 

Edited September 2, 2019 by Ghideon
Added hint

[KFS]

8 hours ago, Ghideon said:

It looks like the problem could have been based on other number but author picked x=8.

Isn't θ is the angle at the lighthouse L between lines LQ and LP? Then x=8 is the opposite and 10 is the adjacent.
tanθ=opposite/adjacent or tanθ=x/10 so x=10tanθ

Hint regarding the derivatives: are you familiar with the chain rule for computing the derivative of the composition of two (or more) functions?

 

Thanks for the help. Yes, I am familiar with composition of functions and the chain rule. It's just that word problems are hard for me.