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MATH / In triangle ABC, ∠A, ∠B, and ∠C form an arithmetic sequence. The length of the altitude from B to (AC)¯ is equal to AB−BC. Find all possible values of sin(C−A)/(2).Enter all possib…

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problem

In triangle ABC,ABC, ∠A,\angle A, ∠B,\angle B, and ∠C\angle C form an arithmetic sequence. The length of the altitude from BB to AC¯\overline{AC} is equal to AB−BC.AB - BC. Find all possible values of sinC−A2.\sin \frac{C - A}{2}.Enter all possible values, separated by commas.
Plain-text mathematical notation (without MathML)
In triangle ABC, ∠A, ∠B, and ∠C form an arithmetic sequence.  The length of the altitude from B to (AC)¯ is equal to AB−BC.  Find all possible values of
sin(C−A)/(2).Enter all possible values, separated by commas.
Original LaTeX notation
In triangle $ABC,$ $\angle A,$ $\angle B,$ and $\angle C$ form an arithmetic sequence.  The length of the altitude from $B$ to $\overline{AC}$ is equal to $AB - BC.$  Find all possible values of
\[\sin \frac{C - A}{2}.\]Enter all possible values, separated by commas.

level

Level 5

type

Precalculus

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Source and history

task_id
592959f0-5b07-50de-aaec-ddbd668fac74
task_key
precalculus--test--592959f0-5b07-50de-aaec-ddbd668fac74
task_revision_id
1
config / split
precalculus / test

Official source

initial import