a guy wire 27 feet long runs from the top of the pole to a spot on the ground. I f the height of the pole is 6 feet longer than the from the base of the pole to the spot where the guy wire is anchored, how tall is the pole?
let x = distance from pole to spot on ground where
guy wire is attached
x + 6 = height of pole
x^2 + ( x+ 2 )^2 = 27^2
simplify and solve for x
Ooooops!
x^2 + (x + 6)^2 = 27^2
Don't know where I got x+ 2.
Sorry.
To find the height of the pole, we can set up a right triangle using the given information. Let's consider the height of the pole to be represented by 'x'.
According to the problem, the length of the guy wire is 27 feet, which is the hypotenuse of the right triangle. The base of the right triangle is the distance from the base of the pole to the spot where the guy wire is anchored, which is 'x - 6'.
Using the Pythagorean theorem, we can write:
(base)^2 + (height)^2 = (hypotenuse)^2
Substituting the given values, we get:
(x - 6)^2 + x^2 = 27^2
Simplifying this equation, we have:
x^2 -12x + 36 + x^2 = 729
2x^2 - 12x - 693 = 0
Now, to solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = -12, and c = -693. Plugging in these values, we have:
x = (-(-12) ± √((-12)^2 - 4 * 2 * -693)) / (2 * 2)
Simplifying the equation further, we get:
x = (12 ± √(144 + 5544)) / 4
x = (12 ± √5688) / 4
Now, to find the value of 'x', we need to calculate the square root of 5688. The square root can be evaluated using a calculator or by using estimation techniques.
Using a calculator, we find that the square root of 5688 is approximately 75.43.
Substituting this value back into the equation for 'x', we have two possible solutions:
x = (12 + 75.43) / 4 ≈ 22.86
or
x = (12 - 75.43) / 4 ≈ -15.86
Since the height of the pole cannot be negative, we can conclude that the height of the pole is approximately 22.86 feet.
Is this really a college question? Seems too easy.
Let x represent the base of the triangle (pole to spot where the wire is). Since you said that the height of the pole is 6 feet longer than the base of the pole to where the wired is anchored. Now 6+x. 27 is the hypotenuse. Use a^2+b^2=c^2 and plug in the numbersnumbers, 29-x=6+x, do the rest and the answer will be 11.5 for x. Now add to 6, which will be 17.5.