Question

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. What is the distance between the points a and b on the flagpole?

1) 3.66 feet
2) 13.66 feet
3) 8.66 feet
4) 5 feet

Answer 1

To find the distance between points a and b on the flagpole, use trigonometry. The distance is found by using the sine function to find the length of the rope dc and then using the sine function again to find the distance between points a and b.

Step-by-step explanation:

To find the distance between points a and b on the flagpole, we can use trigonometry. Since angle adc measures 45 degrees and angle bdc measures 30 degrees, we can use the sine function to find the length of the rope dc. The length of dc is 5 multiplied by the square root of 3, so dc = 5sqrt(3).

Next, we can use the sine function again to find the distance between points a and b. By considering triangle adc, the sine of angle adc is equal to the opposite side (dc) divided by the hypotenuse (ac). So, sin(45) = dc/ac. Rearranging the equation, we get ac = dc/sin(45). Plugging in the values, ac = (5sqrt(3))/(sqrt(2)/2) = 5sqrt(3)*2/sqrt(2) = 10 feet. Therefore, the distance between points a and b on the flagpole is 10 feet.