Question

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

Answer 1

Let length of wire be x

$\\ \tt\Rrightarrow cos\theta=\dfrac{Base}{Hypotenuse}$

$\\ \tt\Rrightarrow cos80=\dfrac{50}{x}$

$\\ \tt\Rrightarrow x=\dfrac{50}{cos80}$

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

$\\ \tt\Rrightarrow x=294ft$

Answer 2

Answer:

☑ Length of wire is approximately 288 ft

☑ Height of antenna is approximately 284 ft

Step-by-step explanation:

» Length of the wire (hypotenuse):

• From trigonometric ratios;

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

» Height of antenna:

${ \tt{ \tan( \theta) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan(80 \degree) = \frac{height}{50} }} \\ \\ { \tt{h = 50 \times \tan(80 \degree) }} \\ \\ { \boxed{ \tt{h = 283.6 \: ft}}}$