A smokestack is 190 ft high. A guy wire must be fastened to the stack 20.0 ft from the top. The guy wire makes an angle of 37.0° with the ground. Find the length of the guy wire. Use significant figures.
I did:
190 - 20 = 170
170/w=sin 37
w=170/sin37
w= -264.16461
the question said used significant figures so my answer is -264.16
is my answer correct?
First of all, take your calculator off Radians (RAD) and make sure you are in
degrees (DEG).
(How did you not realize that a negative result from sin 37° would not make any sense?)
All the data given contains 3 digits, so use 3 digits in your answer once to get
the new result.
No, your answer is not correct. The length of a guy wire cannot be negative.
To find the correct length of the guy wire, you can use the formula:
length of guy wire = height of smokestack / sin(angle)
In this case, the height of the smokestack is 190 ft and the angle is 37.0°.
Plugging in these values, we have:
length of guy wire = 190 ft / sin(37.0°)
Calculating this, we get:
length of guy wire = 190 ft / 0.6018
length of guy wire ≈ 315.66 ft
Rounding to the correct number of significant figures, the length of the guy wire is 316 ft.
Your approach to solving the problem is correct, but there seems to be a mistake in your calculations. Let's go through the steps again and find the correct answer.
First, you correctly found the height from the attachment point to the ground:
190 ft - 20 ft = 170 ft
Next, you used the sine function to find the length of the guy wire. However, it seems like you made an error in your calculation.
The correct equation to use is:
w = 170 ft / sin(37°)
Using a calculator, you can find the value:
w ≈ 278.61 ft
So, the correct length of the guy wire, rounded to three significant figures, is approximately 278 ft.