Answer:
794.19 feet.
Step-by-step explanation:
Please find the attachment.
Let x be the distance helicopter needs to fly to be directly over the tower.
We have been given that a helicopter flying 3590 feet above ground spots the top of a 150-foot y'all cell phone tower at an angle of depression of 77°.
We can see from our attachment that helicopter, tower and angle of depression forms a right triangle.
As height of tower is 150 feet, so the vertical distance between helicopter and tower will be [tex]3590-150=3440[/tex] feet.
We cab see from our attachment that the side with length 3590-150 feet is opposite and side x is adjacent side to 77 degree angle.
Since we know that tangent relates the opposite side of a right triangle to its adjacent side, so we will use tangent to find the length of x.
[tex]\text{Tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{Tan}(77^o)=\frac{3590-150}{x}[/tex]
[tex]\text{Tan}(77^o)=\frac{3440}{x}[/tex]
[tex]x=\frac{3440}{\text{Tan}(77^o)}[/tex]
[tex]x=\frac{3440}{4.331475874284}[/tex]
[tex]x=794.1865\approx 794.19[/tex]
Therefore, the helicopter must fly approximately 794.19 feet to be directly over the tower.
