Question

What is the range of possible sizes for side xxx? One Side is 8.5 the other is 8.0 whats the possible side for x?

Answer 1

`color(blue)(0.5< c <16.6)`

Explanation:

I assume we are talking about a triangle here.

Let `a=8` and `b=8.5`

Let the angle between `bba and bb(b)` be `theta`

Let the unknown side be `bbc`

As `theta->0` ,`color(white)(88)c->0.5`

As `theta->180^@` , `color(white)(88)c->16.5`

So the lenght of side `bbc` will be in the interval:

`0.5< c <16.6`

The above can be seen from the diagram.

Top:

As `theta` approaches `0` , `a+c` becomes close to equaling b.

It can never equal b, because `theta` can never equal 0, if a triangle is to exist. Hence `c>b-a`

Likewise:

Bottom.

As `theta` approaches `180^@`, `bbc` approaches the sum `a+b`, `theta` can never equal `180^@` if a triangle is to exist, so `bbc` never equals `a+b`. Hence `c < a+b`