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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?

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brandoncarroll16
The right triangle with  angle  45 ° has adjacent leg 9 feet
So the opposite leg is calculated from
tan 45 = opposite leg / adjacent leg ⇒ adjacent leg = 9 tan 45 = 9.
That is the distance bc.
The right triangle with angle 60° has adjacent leg 9 and opposite leg (x+9), where x is the distance ab.
Then tan(60) = (x+9) / 9 ⇒x+9 = 9 tan(60)
x + 9 = 15.59
x = 15.59 - 9 = 6.59
Answer: 6.59 feet 

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