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In rhombus ABCD, diagonals AC and BD meet at point E. If the measure of angle DAB is 46 degrees, find the length of EB.
The length of each side of the rhombus is 4 inches.

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sqdancefan

Answer:

  EB ≈ 1.563 in

Step-by-step explanation:

The diagonals of a rhombus divide the figure into four congruent right triangles. Angle DAB is bisected by EA, so angle EAB is 46°/2 = 23°. EB is the side opposite, so the relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(EAB) = EB/AB

  EB = (4 in)sin(23°) . . . . . . multiply by the hypotenuse

  EB ≈ 1.563 in

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