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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:Flagpole45°*<30DI5/3 feetAngle ADC measures 45° and angle DC measures 30°. What is the distance between the points A and B on the flagpole? (1 point)

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 belowFlagpole45lt30 class=

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ANSWER

[tex]\begin{equation*} 3.66\text{ feet} \end{equation*}[/tex]

EXPLANATION

We want to find the distance between points A and B i.e. AB.

To do this, we have to find the lengths of AC, and BC and then, find the difference between them:

[tex]AB=AC-BC[/tex]

To find the length of BC, apply trigonometric ratios, SOHCAHTOA, for triangle DBC for tangent:

[tex]\begin{gathered} \tan30=\frac{opposite}{adjacent} \\ \\ \tan30=\frac{BC}{5\sqrt{3}} \\ \\ BC=5\sqrt{3}*\tan30 \\ \\ BC=5\text{ }ft \end{gathered}[/tex]

To find the length of AC, apply trigonometric ratios, SOHCAHTOA, for triangle DAC for tangent:

[tex]\begin{gathered} \tan(45)=\frac{AC}{5\sqrt{3}} \\ \\ \tan45=\frac{AC}{5\sqrt{3}} \\ \\ AC=5\sqrt{3}*\tan45 \\ \\ AC=8.66\text{ }ft \end{gathered}[/tex]

Therefore, the distance between points A and B is:

[tex]\begin{gathered} AB=8.66-5 \\ \\ AB=3.66\text{ feet} \end{gathered}[/tex]

That is the answer.