Math

A smokestack is 150
feet high. A guy wire must be fastened to the stack
40
feet from the top. The guy wire makes an angle of 40∘
with the ground. Find the length of the guy wire rounded to the nearest foot.

- I've got no idea where to start or what to do. I understand that it is 150 high, but do we add on the other 40 to that? It seems that there are two equations going on, overall I am just very confused. Please and thank you for any help.

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  1. this is trig

    the wire is fastened 40 feet BELOW the top ... how high up?

    the wire is the hypotenuse of a right triangle
    ... you know the length of one side (height of attachment point)
    ... you know the angle with the ground

    draw a sketch

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  2. Read carefully, the wire is attached 40 ft from the top, so the wire is attached 110 ft above the ground.
    So now it becomes very simple, a right-angled triangle with base angle of 40°, and an opposite side of 110 ft.
    We want the hypotenuse h, so
    sin40° = 110/h

    solve for h, see how easy it becomes ?
    (let me know what you get)

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