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 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?

40 feet

20 feet

30 feet

10 feet

Answer 1

so it's tangent?

Answer 2

the short side of that large triangle is \(10\sqrt3\) so the long side is \(10\sqrt3\times \sqrt3=30\)

Answer 3

i'm so confused what

Answer 4

in other words \(AC=30\)

Answer 5

you have two triangles
lets forget about trig, and concentrate on the large triangle
the ratios of a 30 -60 - 90 triangle are
\[1:\sqrt3:2\] for
short side : long side : hypotenuse

your short side is \(10\sqrt3\) so the long side is \(10\sqrt3\times \sqrt3=30\) i.e.
\[AC=30\]

Answer 6

this isn't making any sense to me

Answer 7

sorry

Answer 8

so \(AC=30\) but that doesn't answer the question because you don't want \(AC\)

Answer 9

you want \(AB=AC-BC=30-10=20\)

Answer 10

ok but what would the answer be

Answer 11

20

Answer 12

thank you!