Answer: [tex]x\approx182\ ft[/tex]
Step-by-step explanation:
For this exercise you need to use the following Trigonometric Identity:
[tex]cos\alpha =\frac{adjacent}{hypotenuse}[/tex]
Observe the Right triangle BCD given in the exercise. You can identify that, in this case:
[tex]\alpha =\angle C=77\°\\\\adjacent=CD=41\ ft\\\\hypotenuse=BC=x[/tex]
Knowing these values, you can substitute them into [tex]cos\alpha =\frac{adjacent}{hypotenuse}[/tex], as below:
[tex]cos(77\°)=\frac{41}{BC}[/tex]
The next step is to solve for "x" in order to find its value:
[tex]x*cos(77\°)=41\\\\x=\frac{41}{cos(77\°)}\\\\x=182.26\ ft[/tex]
Finally, rounded the result to the nearest foot, you get that this is:
[tex]x\approx182\ ft[/tex]
