It is easier to solve the exercise if you first draw the situation posed by the statement:
Now, you can find the measure of the cell tower using the following ratio:
[tex]\begin{gathered} \frac{8\text{ ft}}{4\text{ ft}}=\frac{\text{ cell tower}}{37\text{ ft}} \\ \text{ Because the distance from the cell tower to the stake is 33ft + 4ft = 37ft} \\ \frac{8}{4}=\frac{\text{ cell tower}}{37\text{ ft}} \\ 2=\frac{\text{ cell tower}}{37\text{ ft}} \\ \text{ Multiply by 37 ft from both sides of the equation} \\ 2\cdot37\text{ ft}=\frac{\text{ cell tower}}{37\text{ ft}}\cdot37\text{ ft} \\ 74\text{ ft = cell tower} \end{gathered}[/tex]
Finally, since the cell tower, the ground, and the guy wire form a right triangle, then you can use the Pythagorean Theorem to find the length of the guy wire:
[tex]\begin{gathered} a^2+b^2=c^2\text{ }\Rightarrow\text{ Pythagorean Theorem} \\ \text{ Where a and b are the legs and} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]
Then, you have
[tex]\begin{gathered} a=37\text{ ft} \\ b=74ft \\ c=\text{?} \end{gathered}[/tex][tex]\begin{gathered} a^2+b^2=c^2 \\ (37\text{ ft})^2+(74\text{ ft})^2=c^2 \\ 1369\text{ ft}^2+5476\text{ ft}^2=c^2 \\ 6845ft^2=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{6845ft^2}=\sqrt[]{c^2} \\ 82.7ft=c \\ \text{ Rounding to the nearest foot} \\ 83\text{ ft }=c \end{gathered}[/tex]
Therefore, the length of the guy wire is approximately 83 feet.
