Question

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

Answer 1

Answer:

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: