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
13.66 feet
8.66 feet
5 feet

Given that the measure of ∠ADC = 45° and ∠BDC = 30° and the length of DC is 5√3 feet

We need to determine the distance between the points A and B on the flagpole.

Distance between BC:

The distance between BC can be determined using the Pythagorean theorem.

Thus, we have;

Substituting the values, we get;

Simplifying, we get;

Thus, the length of BC is 5 feet.

Distance between AB:

The distance between AB can be determined using the Pythagorean theorem.

Thus, we have;

Substituting the values, we get;

Simplifying, we get;

Thus, the distance between AB is 3.66 feet

Hence, Option A is the correct answer.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500