Question

4. A cell phone tower is anchored by 2 cables for support. They stretch from the top of the tower to the ground. The angle of depression from the top of the tower to the point at which the cable reaches the ground is 23°, and distance from the bottom of the tower to the point at which the cable reaches the ground is 60 feet. How long is the cable?

Answer 1

Let's begin by identifying key information given to us:

We are given one known angle & one known side

`\theta=23^(\circ),adjacent=60ft,hypotenuse=\text{?}`

We will solve using Trigonometric Ratio (SOHCAHTOA) & in this case, CAH:

`\begin{gathered} CAH\Rightarrow cos\theta=(adjacent)/(hypotenuse) \\ cos\theta=(adjacent)/(hypotenuse) \\ cos23^(\circ)=(60)/(hypotenuse) \\ hypotenuse\cdot cos23^(\circ)=60 \\ hypotenuse=(60)/(cos23^(\circ))=(60)/(0.9205) \\ hypotenuse=65.18\approx65 \\ hypotenuse=65ft \end{gathered}`

Therefore, the cable is 65 feet long