D.perpendicular cross section of a pyramid cone
69 and 69 makes 69 hahahaha
Answer:
is A
Step-by-step explanation:
Answer:
<em>The shortest possible length for the service road is 2.88 miles.</em>
Step-by-step explanation:
According to the below diagram,
and
are the positions of airport, shopping center and factory respectively.
Given that,
and ![AC= 6.0 miles](https://tex.z-dn.net/?f=AC%3D%206.0%20miles)
In right triangle ![ABC](https://tex.z-dn.net/?f=ABC)
![tan(\angle ACB)=\frac{AB}{BC} \\ \\ tan(\angle ACB)= \frac{3.6}{4.8}=0.75\\ \\ \angle ACB= tan^-^1(0.75)=36.8698.... degree](https://tex.z-dn.net/?f=tan%28%5Cangle%20ACB%29%3D%5Cfrac%7BAB%7D%7BBC%7D%20%5C%5C%20%5C%5C%20tan%28%5Cangle%20ACB%29%3D%20%5Cfrac%7B3.6%7D%7B4.8%7D%3D0.75%5C%5C%20%5C%5C%20%5Cangle%20ACB%3D%20tan%5E-%5E1%280.75%29%3D36.8698....%20degree)
The shortest possible length for the service road from the shopping center to the highway that connects the airport and factory is
.
That means,
is also a right triangle in which
, Hypotenuse
miles and
is the opposite side in respect of
or
.
Now in right triangle ![BCD](https://tex.z-dn.net/?f=BCD)
![Sin(\angle ACB)=\frac{BD}{BC}\\ \\ Sin(36.8698...)=\frac{BD}{4.8}\\ \\ BD=4.8*Sin(36.8698...)=2.88](https://tex.z-dn.net/?f=Sin%28%5Cangle%20ACB%29%3D%5Cfrac%7BBD%7D%7BBC%7D%5C%5C%20%5C%5C%20Sin%2836.8698...%29%3D%5Cfrac%7BBD%7D%7B4.8%7D%5C%5C%20%5C%5C%20BD%3D4.8%2ASin%2836.8698...%29%3D2.88)
So, the shortest possible length for the service road is 2.88 miles.