Question

agpole, 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 60 degrees and angle BDC measures 30 degrees. The length of DC is 5 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?

20 feet
15 feet
10 feet
25 feet

Answer 1

We only need to find the heights of the 2 points on the flagpole and then subtract them. We have that AC and DC are related by the following trigonometric number: tan60=AC/DC. This is because ADC is a right triangle and AC is the opposite leg of the angle we know, while DC is the adjacent leg.
$tan60= \sqrt{3} =AC/5 \sqrt{3} \\ AC=5 \sqrt{3} * \sqrt{3} =5*3=15$.

Thus, we have calculated AC. The same remarks apply to the triangle BCD; However, now we get that tan30=BC/DC.
$tan60= 1/\sqrt{3} =BC/5 \sqrt{3} \\ BC=5 \sqrt{3} / \sqrt{3} =5$.


Hence, the height of point B is 5 feet, while the height of point A is 15 feet. Their distance is 10 feet.