Question

Could someone please help? I’m at a pre calculus level, thanks!

Answer 1

Let length of wire be x

`\\ \tt\Rrightarrow cos\theta=(Base)/(Hypotenuse)`

`\\ \tt\Rrightarrow cos80=(50)/(x)`

`\\ \tt\Rrightarrow x=(50)/(cos80)`

`\\ \tt\Rrightarrow x=50/0.17`

`\\ \tt\Rrightarrow x=294ft`

Answer 2

☑ Length of wire is approximately 288 ft

☑ Height of antenna is approximately 284 ft

Explanation:

» Length of the wire (hypotenuse):

• From trigonometric ratios;

`{ \tt{ \cos( \theta) = (adjacent)/(hypotenuse) }} \\ \\ { \tt{ \cos(80 \degree) = (50)/(length) }} \\ \\ { \tt{length = (50)/( \cos(80 \degree) ) }} \\ \\ { \boxed{ \tt{l = 287.9 \: ft}}}`

» Height of antenna:

`{ \tt{ \tan( \theta) = (opposite)/(adjacent) }} \\ \\ { \tt{ \tan(80 \degree) = (height)/(50) }} \\ \\ { \tt{h = 50 * \tan(80 \degree) }} \\ \\ { \boxed{ \tt{h = 283.6 \: ft}}}`