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alisha [4.7K]
3 years ago
15

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 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?

Mathematics
2 answers:
BigorU [14]3 years ago
6 0
You have two 30-60-90 triangles, ADC and BDC.

The ratio of the lengths of the sides of a 30-60-90 triangle is

short leg : long leg : hypotenuse
     1        :  sqrt(3)  :        2

Using triangle ADC, we can find length AC.
Using triangle BDC, we can find length BC.
Then AB = AC - BC

First, we find length AC.
Look at triangle ACD.
DC is the short leg opposite the 30-deg angle.
DC = 10sqrt(3)
AC = sqrt(3) * 10sqrt(3) = 3 * 10 = 30

Now, we find length BC.
Look at triangle BCD.
For triangle BCD, the long leg is DC and the short leg is BC.
BC = 10sqrt(3)/sqrt(3) = 10

AB = AC - BC = 30 - 10 = 20
aev [14]3 years ago
5 0

Answer:

the answer is 20 took the test

Step-by-step explanation:

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Answer:

  0, for q ≠ 0 and q ≠ 1

Step-by-step explanation:

Assuming q ≠ 0, you want to find the value of x such that ...

  q^x = 1

This is solved using logarithms.

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  x·log(q) = log(1) = 0

The zero product rule tells us this will have two solutions:

  x = 0

  log(q) = 0   ⇒   q = 1

If q is not 0 or 1, then its value is 1 when raised to the 0 power. If q is 1, then its value will be 1 when raised to <em>any</em> power.

_____

<em>Additional comment</em>

The applicable rule of logarithms is ...

  log(a^b) = b·log(a)

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Area of a triangle: L x W
———
2

Area of a square: L x W


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