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

40 feet

20 feet

30 feet

10 feet

ans=20 feet

Step-by-step explanation: in triangle ACD,

tan60=AC/10*(sqrt(3)) {since tan= AC/DC}

also tan60=sqrt(3)

therefore sqrt(3)=AC/10*(sqrt(3))

then AC=sqrt(3)*sqrt(3)*10

hence, AC=30 feet (1)

similarly,

in triangle BCD,

tan30=BC/DC

tan30=1/sqrt(3)

hence, 1/sqrt(3)=BC/10*(sqrt(3))

hence, 10*(sqrt(3))/sqrt(3)=BC

therefore BC=10 feet (2)

distance between A and B = AC-BC

                                             =(30-10) feet {from (1) and(2)}

distance between A and B  = 20 feet

therefore, distance between A and B is 20 feet

-2 is the right

answer for #1 is c

answer for #2 is d

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