3 years ago

The exact length of line segment AB is?

Mathematics

1 answer:

DanielleElmas [232]3 years ago

5 0

Answer:

6in

Step-by-step explanation:

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A guy wire to a tower makes a 72 degrees angle with level ground. At a point 30 ft farther from the tower than the wire but on t

Andreyy89

So.. checking the picture below

we can say y = y, or just do a substitution and end up with

$\bf tan(72^o)=tan(30^o)(30+x)\implies 3.08x=\cfrac{30}{\sqrt{3}}+\cfrac{1}{\sqrt{3}}x
\\\\\\
3.08x-\cfrac{1}{\sqrt{3}}x=\cfrac{30}{\sqrt{3}}\implies 2.5x\approx 17.32\implies x\approx \cfrac{17.32}{2.5}$

once you know, how long is "x", then you can simply use the cosine of 72° to get "r"

thus $\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad cos(72^o)=\cfrac{x}{r}\implies r=\cfrac{x}{cos(72^o)}$