Question

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:Angle ADB measures 60°, and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?

Answer 1

Answer: 10 ft

Explanation

As two right triangles (a triangle with a 90º angle) are formed, to know the distance between AB we have to calculate BC, AC and subtract.

0. Calculating BC

We have a 30º angle and an adjacent side 5√3ft (as the hypotenuse is the side opposite to the 90º angle). Thus, using the tangent function where:

$\tan\theta=\frac{opposite}{adjacent}$

we can find the opposite side, which is BC. Replacing the values and simplifying we get:

$\tan(30\degree)=\frac{BC}{5\sqrt{3}}$$BC=5\sqrt{3}\tan(30\degree)$$BC=5ft$

Thus, the segment BC measures 5ft.

2. Calculating segment AC.

In this case, our hypotenuse changes. However, we are still looking for the opposite side. Using the tangent function as before we get:

$AC=5\sqrt{3}\tan(60\degree)$$AC=15$

3. Calculating the distance between A and B

$AC-BC=15-5=10ft$