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: angle adc measures 60°, and angle bdc measures 30°. what is the distance between the points a and b on the flagpole? (1 point) 20 feet 15 feet 10 feet 5 feet

Explanation:

Step1: Calculate length of AC

$\tan(60^\circ) = \frac{AC}{DC}$
$AC = DC \times \tan(60^\circ) = 5\sqrt{3} \times \sqrt{3} = 5 \times 3 = 15$ feet

Step2: Calculate length of BC

$\tan(30^\circ) = \frac{BC}{DC}$
$BC = DC \times \tan(30^\circ) = 5\sqrt{3} \times \frac{1}{\sqrt{3}} = 5$ feet

Step3: Find distance AB

$AB = AC - BC$

Answer:

10 feet