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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 ADB measures 60 degrees and angle BDC measures 30 degrees. The length of DC is 10 multiplied by square root of 3. Angle ADC measures 60° and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?

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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mathstudent55

Answer:

AB = 20 ft

Step-by-step explanation:

DC = 10√3 ft

Triangle BCD is a right triangle with angles measuring 30°-60°-90°.

The ratio of the lengths of BC to CD is 1:√3.

BC = (10√3)/√3 ft = 10 ft

Triangle ACD is a right triangle with angles measuring 30°-60°-90°.

The ratio of the lengths of DC to AC is 1:√3.

AC = 10√3 × √3 ft = 30 ft

AB = AC - BC

AB = 30 ft - 10 ft

AB = 20 ft

aksnkj

The distance between points A and B on the flagpole is 20 feet.

Given information:

Two ropes, AD and BD, are tied to a peg on the ground at point D.

Angle ADB measures 60 degrees and angle BDC measures 30 degrees.

The length of DC is [tex]10\sqrt3[/tex] ft.

It is required to calculate the distance between A and B.

Now, use trigonometric ratios to calculate the value of AB as,

[tex]tan60=\dfrac{AC}{DC}\\\sqrt3=\dfrac{AC}{10\sqrt3}\\AC=30[/tex]

Also,

[tex]tan30=\dfrac{BC}{DC}\\\dfrac{1}{\sqrt3}=\dfrac{BC}{10\sqrt3}\\BC=10[/tex]

So, the value of AB will be calculated as,

[tex]AB=AC-BC\\AB=30-10\\AB=20\rm\; ft[/tex]

Therefore, the distance between points A and B on the flagpole is 20 feet.

For more details, refer to the link:

https://brainly.com/question/23428230