Answer with Step-by-step explanation:
We are given that
Height of radio tower =650 ft
From figure
AB=650 ft
BC=180 ft
We have to find the AC.
Using cosine law:
[tex]c=\sqrt{a^2+b^2-2ab cos\alpha}[/tex]
[tex]AC=\sqrt{(650)^2+(180)^2-2\times 650\times 180\times cos 80^{\circ}}[/tex]
[tex]c=643.64 ft[/tex]
Hence, a guy required 643.64 ft wire when it is to connect to the tower and be secured at a point on the sloped side 180 ft from the base of the tower.
b.In a right triangle ABC, AB=[tex]\frac{650}{2}=325 ft [/tex]
Pythagorous theorem :[tex](Hypotensuse)^2=(perpendicular\;side)^2+(base)^2[/tex]
Substitute the values
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
[tex](AC)=\sqrt{(325)^2+(180)^2}[/tex]
[tex]AC=371.52 ft [/tex]
Hence, the length of wire should be 371.52 ft when a second guy connect the middle of the tower and be secured at a point 180 ft from the base on the flat side by wire.
