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Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole, as shown below: Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole. Angle ADC measures 45 degrees and angle BDC measures 30 degrees. The length of DC is 5 multiplied by square root of 3. Angle ADC measures 45° and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?

3.66 feet

6.34 feet

1.55 feet

2.74 feet

Two ropes AD and BD are tied to a peg on the ground at point D The other ends of the ropes are tied to points A and B on a flagpole as shown below Two ropes AD class=

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sqdancefan

Answer:

  3.66 feet

Step-by-step explanation:

The tangent of an angle is the ratio of the opposite side to the adjacent side:

  Tan = Opposite/Adjacent

In the case of your triangle, this means ...

  tan(45°) = AC/DC

  AC = DC×tan(45°)

and

  tan(30°) = BC/DC

  BC = DC×tan(30°)

The length of interest is ...

  AB = AC - BC = DC×tan(45°) -DC×tan(30°)

  AB = DC×(tan(45°) -tan(30°)) = 5√3×(1 - 1/√3)

  AB = 5(√3 -1) ≈ 3.66 . . . . . feet