Question

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° how far must the helpicopter fly to be directly over the tower

Answer 1

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 $3590-150=3440$ 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.

$\text{Tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

Upon substituting our given values in above formula we will get,

$\text{Tan}(77^o)=\frac{3590-150}{x}$

$\text{Tan}(77^o)=\frac{3440}{x}$

$x=\frac{3440}{\text{Tan}(77^o)}$

$x=\frac{3440}{4.331475874284}$  

$x=794.1865\approx 794.19$

Therefore, the helicopter must fly approximately 794.19 feet to be directly over the tower.