Question

A support cable runs from the top of a telephone pole to a point on the ground 42.7 feet from its base. Suppose the cable makes an angle of 29.6 with the ground (as shown in the following figure).(a) Find the height of the pole. (Round the answer to the nearest tenth.) feet (b) Find the length of the cable. (Round the answer to the nearest tenth.) feet

Answer 1

We will draw a sketch to see the position of the cable

From the figure, we can use the tangent ratio to find the height

`(h)/(42.7)=tan(29.6)`

By using the cross-multiplication

`\begin{gathered} h=42.7tan(29.6) \\ \\ h=24.3\text{ feet} \end{gathered}`

a) The height of the pole is 24.3 feet to the nearest tenth

To find the length of the cable we will use the cosine ratio

`cos(29.6)=(42.7)/(L)`

Switch L and cos(29.6)

`\begin{gathered} L=(42.7)/(cos(29.6)) \\ \\ L=49.1\text{ feet} \end{gathered}`

b) The length of the cable is 49.1 feet to the nearest tenth