Question

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.

Answer 1

EB ≈ 1.563 in

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