A smokestack is 180 ft high. A guy wire must be fastened to the stack 30.0 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:
180ft - 30ft =150ft
sin 37 = 150/x
x=150/sin 37
x= 249.2460212
how do I the significant figures for my answer: 249.2460212 ?
150 feet up
sin 37.0 = 150 / hypotenuse which is the wire
so yes
150/ sin 37.0
you were only given the height to the nearest foot so I would say 249 feet
but what if it were sin 37.1 instead of 37.0
then I would get 248.6
well that is still 249 :)
To determine the significant figures in your answer, you need to consider the significant figures in the given values.
In this case, the value 30.0 ft has three significant figures.
Since the angle is given as 37.0°, it also has three significant figures.
However, the height of the smokestack is given as 180 ft, which is an exact value and therefore has an infinite number of significant figures.
When performing calculations with multiple numbers, it is standard practice to round the final answer to match the least number of significant figures in any of the given values.
Therefore, the length of the guy wire should be rounded to three significant figures, which means your final answer is approximately 249 ft.
To determine the significant figures in your answer, you should consider the given number of significant figures in the initial measurements provided in the question. In this case, the height of the smokestack is specified as exactly 180 ft, so there are three significant figures in this measurement.
Since the angle of 37.0° is given to the nearest degree (which implies some uncertainty), it is appropriate to use this value to determine the number of significant figures in your result. In general, when using trigonometric functions like sine, the number of significant figures should not exceed the number of significant figures in the angle measurement.
Therefore, you should round your answer to three significant figures. The number 249.2460212 can be rounded to 249, as the last digit, 6, is greater than 5.
Hence, the length of the guy wire, using three significant figures, is 249 ft.