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MATH / In triangle ABC, D and E are on side (BC)¯ such that BD=DE=EC. If x=∠BAD, y=∠DAE, and z=∠EAC, then find (sin(x+y)sin(y+z))/(sinxsinz).

Problem

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problem

In triangle ABC,ABC, DD and EE are on side BC¯\overline{BC} such that BD=DE=EC.BD = DE = EC. If x=∠BAD,x = \angle BAD, y=∠DAE,y = \angle DAE, and z=∠EAC,z = \angle EAC, then find sin(x+y)sin(y+z)sinxsinz.\frac{\sin (x + y) \sin (y + z)}{\sin x \sin z}.
Plain-text mathematical notation (without MathML)
In triangle ABC, D and E are on side (BC)¯ such that BD=DE=EC.  If x=∠BAD, y=∠DAE, and z=∠EAC, then find
(sin(x+y)sin(y+z))/(sinxsinz).
Original LaTeX notation
In triangle $ABC,$ $D$ and $E$ are on side $\overline{BC}$ such that $BD = DE = EC.$  If $x = \angle BAD,$ $y = \angle DAE,$ and $z = \angle EAC,$ then find
\[\frac{\sin (x + y) \sin (y + z)}{\sin x \sin z}.\]

level

Level 5

type

Precalculus

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Source and history

task_id
69d3f1ac-1b19-52be-900c-bcec6d2fcc87
task_key
precalculus--test--69d3f1ac-1b19-52be-900c-bcec6d2fcc87
task_revision_id
1
config / split
precalculus / test

Official source

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