Question

Hellpp!!!

Answer 1

If mBC is real, then there is an infinite number of possible values.
If mBC is integer (i.e. counting numbers), then you can work that out using the triangle inequality:
The sum of any two sides of a triangle is greater than the third side, which I can make a corollary as:
The sum of the two shorter sides of a triangle must be greater than the third side.
But here you have another constraint, which is the sum of the two base angles must not be obtuse.

Answer 2

From the diagram, we see that (x+y)<90 degrees is another constraint, this means that angle D must be obtuse.
The Pythagoras theorem will express this inequality as:
(mBC)^2>8^2+15^2
This provides the lower bound of mBC, while the triangle inequality gives the upper bound.

Answer 3

then mBC>17; 7<mBC<23; 17<mBC<23 there are 6 values then is it true?
but the answer key says it's 5

Answer 4

@mathmate

Answer 5

:)