Related Rates: Trig Homework Solving x when Theta Increases

[kLPantera]

Homework Statement

If theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per measure at the instant when x equals 3 units?

The Attempt at a Solution

I drew the triangle and I came to the conclusion that I needed to use 5sin(theta)=x

Then I did the derivative and it comes out to 5cos(theta)d(theta)/dt=dx/dt

Here is where I am a little confused, I get cos(theta) = (5/2)√(3)/5 based off of the 30 60 90 triangle.

Am I doing this right? After I do the calculations, I don't get the right answer because no where are you supposed to have a sqrt in the answer.

 

[SammyS]

Homework Statement

If theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per measure at the instant when x equals 3 units?

The Attempt at a Solution

I drew the triangle and I came to the conclusion that I needed to use 5sin(theta)=x

Then I did the derivative and it comes out to 5cos(theta)d(theta)/dt=dx/dt

Here is where I am a little confused, I get cos(theta) = (5/2)√(3)/5 based off of the 30 60 90 triangle.

Am I doing this right? After I do the calculations, I don't get the right answer because no where are you supposed to have a sqrt in the answer.

Please write the complete problem as it was given to you.

I may be able to guess what you're supposed to do, but if my guess is wrong, that won't really help you.

 

[kLPantera]

I typed the problem word for word, I'll include the multiple choice answers in this post:

a) 3
b) 15/4
c)4
d)9
e)12

 

[STEMucator]

This is a related rates problem right? What is dθ/dt? What is dx/dt? Write down all your variables BEFORE you start trying to manipulate things.

 

[SammyS]

I typed the problem word for word, I'll include the multiple choice answers in this post:

a) 3
b) 15/4
c)4
d)9
e)12

If you typed it word for word, as follows, copied & pasted directly from your Original Post, & shown below:

"If theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per measure at the instant when x equals 3 units?"​

then, where does the triangle come from, about which you stated:

"I drew the triangle and I came to the conclusion that I needed to use 5sin(theta)=x"​

??