Question

agpole, as shown below: 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. angle adc measures 60 degrees and angle bdc measures 45 degrees. the length of dc is 9. angle adc measures 60° and angle bdc measures 45°. what is the distance between the points a and b on the flagpole? 6.59 feet 1.73 feet 4.32 feet 2.56 feet

Answer 1

The right triangle with  angle  45 ° has adjacent leg 9 feet

So the opposite leg is calculated from

tan 45 = opposite leg / adjacent leg ⇒ adjacent leg = 9 tan 45 = 9.

That is the distance bc.

The right triangle with angle 60° has adjacent leg 9 and opposite leg (x+9), where x is the distance ab.

Then tan(60) = (x+9) / 9 ⇒x+9 = 9 tan(60)

x + 9 = 15.59

x = 15.59 - 9 = 6.59

Answer: 6.59 feet