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 below:

Angle ADC measures 45 degrees and angle BDC measures 30 degrees. What is the distance between the points A and B on the flagpole?

3.66 feet
6.34 feet
1.55 feet
2.74 feet

Answer 1

You know both angles and the adyacent legs.


Then  you can use the tangent ratio to find the opposite legs.


After that, you can do Distance AB = Distance AC - Distance BC


Let's work:


tan(30°) = BC / [5√3] => BC = 5√3 tan(30°) = 5


tan(45°) = AC / [5√3] => AC = 5√3 tan(45°) = 5√3


=> AC - BC = 5√3 - 5 = 3.66


Answer: 3.66 feet