Answer:
[tex]x\approx 422.4[/tex]
Step-by-step explanation:
Assuming 'x' the distance helicopter needs to fly to be directly over the tower.
It is given that a helicopter flying 3590 feet above ground spots the top of a 150-foot tall cell phone tower at an angle of depression of 83°.
From 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: 3590-150=3440 feet.
Also, the side with length 3590-150 feet is opposite and side x is adjacent side to 83° angle.
As the 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]
[tex]\text{Tan}(83^o)=\frac{3590-150}{x}\\[/tex]
[tex]\text{Tan}(83^o)=\frac{3440}{x}[/tex]
[tex]x=\frac{3440}{\text{Tan}(83^o)}[/tex]=>[tex]x=\frac{3440}{8.14434}[/tex]
[tex]x\approx 422.4[/tex]
Thus, the helicopter must fly approximately 422.4 feet to be directly over the tower.
