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

You have two 30-60-90 triangles, ADC and BDC.

The ratio of the lengths of the sides of a 30-60-90 triangle is

short leg : long leg : hypotenuse

    1        :  sqrt(3)  :        2

Using triangle ADC, we can find length AC.

Using triangle BDC, we can find length BC.

Then AB = AC - BC

First, we find length AC.

Look at triangle ACD.

DC is the short leg opposite the 30-deg angle.

DC = 10sqrt(3)

AC = sqrt(3) * 10sqrt(3) = 3 * 10 = 30

Now, we find length BC.

Look at triangle BCD.

For triangle BCD, the long leg is DC and the short leg is BC.

BC = 10sqrt(3)/sqrt(3) = 10

AB = AC - BC = 30 - 10 = 20

Step-by-step explanation:

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