Question

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

Answer 1

9514 1404 393

Answer:

D 2.14

Explanation:

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.