If x = 34, y = 53, and the measure
of AC = 4 units, what is the difference in length between
segments AB and AD? Round your answer to
the nearest
hundredth.

A- 0.74
B- 1.17
C- 1.64
D- 2.14

The lengths of interest are the hypotenuses of the respective triangles. We are given the angle and the opposite side, so the sine relation is of interest.

Sin = Opposite/Hypotenuse

sin(34°) = AC/AB ⇒ AB = AC/sin(34°)

sin(53°) = AC/AD ⇒ AD = AC/sin(53°)

The desired difference in lengths is ...

AB -AD = AC(1/sin(34°) -1/sin(53°)) = 4(1.78829 -1.25214) ≈ 2.1446

The difference in lengths is about 2.14 units.

If x = 34, y = 53, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth. A- 0.74 B- 1.17 C- 1.64 D- 2.14

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If x = 34, y = 53, and the measure
of AC = 4 units, what is the difference in length between
segments AB and AD? Round your answer to
the nearest
hundredth.

A- 0.74
B- 1.17
C- 1.64
D- 2.14