Question

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?

Answer 1

Answer: 5(√3-1) unit.

Step-by-step explanation:

Since, By the below diagram,

For triangle BDC,

We can write,

$tan 30^{\circ}=\frac{BC}{DC}$

⇒ $\frac{1}{\sqrt{3}}=\frac{BC}{5\sqrt{3}}}$

⇒  $\sqrt{3}=\frac{5\sqrt{3}}{BC}$

⇒ $BC=\frac{5\sqrt{3} }{\sqrt{3} }$

⇒ $BC=5\text{ unit}$

Now, In triangle ADC,

$tan45^{\circ}=\frac{AC}{DC}$

⇒ $1=\frac{AB+BC}{DC}$

⇒ $1=\frac{DC}{AB+BC}$

⇒ $1=\frac{5\sqrt{3}}{AB+5}$

⇒ $AB+5=5\sqrt{3}$

⇒ $AB=5\sqrt{3}-5=5(\sqrt{3}-1)\text{ unit}$

Answer 2

Answer: 3.66 feet

Step-by-step explanation: