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
I agree
Your calculations are correct. The length of the guy wire is 249.25 ft, rounded to four significant figures.
To find the length of the guy wire, you need to first calculate the length of the side opposite to the angle (which is the height of the stack minus the distance from the top where the guy wire is fastened) and then use trigonometry.
In this case, you correctly subtracted the distance from the top (30 ft) from the total height of the stack (180 ft) to get 150 ft.
Next, you used the sine function to set up the trigonometric equation, sin 37 = 150/x, where x represents the length of the guy wire.
To solve for x, you need to isolate it on one side of the equation. So, multiply both sides of the equation by x to remove the denominator:
x * sin 37 = 150
Finally, divide both sides of the equation by sin 37 to solve for x:
x = 150 / sin 37
Evaluating this expression using a calculator, you get approximately 249.25 feet.
The length of the guy wire, rounded to the appropriate number of significant figures, is 249 ft.