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.(will give medal)

Question

anonymous · Answer

Angle ADC measures 45° and angle BDC measures 30°. 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

solomonzelman · Answer

First you can see that the bottom triangle is 30-60-90 triangle, right?

solomonzelman · Answer

So, BC =5

Now....

solomonzelman · Answer

∠DBA= 180-60=120  (Supplementary angles)
so the top angle is then supposed to be equal to 180-(120+45)=15

solomonzelman · Answer

knowing the top angle and the 90 degree angle, you can just look at a big triangle.

solomonzelman · Answer

Now you can solve for the AB.

solomonzelman · Answer

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