Question

two ropes, ad and bd, are tied to a peg on the ground at point d. the other ends of the rope are tied to points, a and b, on a flagpole. angle adc measure 45 degrees and angle bdc measures 30 degrees. IF the distance between point d and the flagpole is 5*the square root of 3 what is the distance between points a and b on the flagpole?

Answer 1

I guess C is the point where the flagpole touches the ground. If so:

ADC is a an isosceles right triangle. (ACD = 90, ADC = 45, then DAC=45).
So DC = AC = 5√3. Now let's consider the right triangle BCD:
ADC = 30, tan 30 = BC/DC:
tan 30 = BC/5√3, or tan30 = √3/3 → √3/3 = BC/5√3 and
BC =5. But AB = AC - BC
AB = 5√3 - 5
AB =5(√3 - 1) or AB = 3.66