Civil an airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. the airport and factory are 6.0 miles apart. their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. a service road will be constructed from the shopping center to the highway that connects the airport and factory. what is the shortest possible length for the service road? round to the nearest hundredth.

The shortest possible length for the service road is 2.88 miles.

Step-by-step explanation:

According to the below diagram, and are the positions of airport, shopping center and factory respectively.

Given that,   and

In right triangle

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

So, the shortest possible length for the service road is 2.88 miles.

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