If sine ⁡theta equals negative 8/17 and the terminal side of theta lies in quadrant iv, find cosine ⁡ theta .

answer:

  a) δdef ~ δged

  b) aa similarity: ∠d≅∠g; ∠e≅∠e

  c) ed = 4

step-by-step explanation:

a) all three of the right triangles in the figure are similar to each other. the ones relevant to the problem are δdef and δged.

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b) any pair of right triangles in the figure shares at least one acute angle. that makes them similar by the aa similarity postulate. for triangles def and ged, the shared acute angle is angle e. the corresponding right angles are ∠d in δdef and ∠g in δged.

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c) corresponding parts of similar triangles are proportional, so we can write

  ed/ef = eg/ed

"cross multiplying" gives

  ed² = ef·eg = 8·2 = 16

  ed = √16

  ed = 4