Question 884590
A telephone perpendicular to the ground. A taut anchoring cable is 60 ft. long runs from the ground to the top of the pole. If the tangent of the angle between the ground and the cable is 2.6, how tall is the pole?
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Draw the picture:
You have a right triangle with hypotenuse = 60 ft.
Let height = "h" ; Let base = "b".
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h/b = 2.6
h^2 + b^2 = 60^2
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b = h/2.6
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Substitute for "b" and solve for "h":
h^2 + (h/2.6)^2 = 60^2
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2.6^2*h^2 + h^2 = (2.6*60)^2
7.76h^2 = (2.6*60)^2
h = 56 ft
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Cheers,
Stan H.