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Answered

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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

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 074 B 117 C class=

Sagot :

Sqdancefanidn

9514 1404 393

Answer:

  D  2.14

Step-by-step 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.

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