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 fl

Question

3 years ago

14

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 fl

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 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?. A. 3.66 feet B.13.66 feet C. 8.66 feet D. 5 feet

Mathematics

1 answer:

Arlecino [84] · Answer 1 · 2022-02-08T19:17:57+03:00

Arlecino [84]3 years ago

8 0

Answer:

A. 3.66 feet

Step-by-step explanation:

Using trigonometry, we know that ...

BC = DC·tan(30°)

AC = DC·tan(45°)

AB = AC -BC = DC(tan(45°) -tan(30°))

AB = 5√3·(1 -√3/3) = 5(√3 -1)

AB ≈ 3.66 . . . feet