Question

tethers to help support a flag pole, a 50-foot-long tether is tied to the pole at a point 40 feet above the ground. the tether is pulled taut and tied to an anchor in the ground. how far away from the base of the pole is the anchor? \boxed{} feet.

Explanation:

Step1: Identify the right triangle

The flag pole, the ground from the base of the pole to the anchor, and the tether form a right triangle. The tether is the hypotenuse ($c = 50$ feet), the height on the pole is one leg ($a = 40$ feet), and the distance from the base to the anchor is the other leg ($b$), which we need to find. We use the Pythagorean theorem: $a^{2}+b^{2}=c^{2}$.

Step2: Substitute values into the formula

Substitute $a = 40$ and $c = 50$ into the formula: $40^{2}+b^{2}=50^{2}$. Calculate $40^{2}=1600$ and $50^{2}=2500$. So the equation becomes $1600 + b^{2}=2500$.

Step3: Solve for $b^{2}$

Subtract 1600 from both sides: $b^{2}=2500 - 1600=900$.

Step4: Solve for $b$

Take the square root of both sides: $b=\sqrt{900}=30$.

Answer:

30