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:
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 45 degrees, and angle bdc measures 30 degrees. the length of dc is 5 multiplied by square root of 3.
angle adc measures 45°, and angle bdc measures 30°. what is the distance between the points a and b on the flagpole?

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.