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, 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 30 degrees. The length of DC is 5 multiplied by square root of 3.

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

Answer 1

can anyone help me out with this

Answer 2

the answer choices are 10, 15, 20, and 25

Answer 3

is C the base of the flagpole..?

Answer 4

i posed a picture of the triangle

Answer 5

so find the length AC using the tan ratio and an angle of 60

then find BC, again using the tan ratio and an angle of 30

the the distance AB is AC - BC

hope it helps

Answer 6

thank you! wait is the answer 10ft?

Answer 7

I don't know I haven't done the calculation

Answer 8

can you walk me through it

Answer 9

ok... so do you know the exact value of tan(30) and tan(60)..?

Answer 10

tan60 is
1.73205080757

Answer 11

tan30 is
0.57735026919

Answer 12

here is the start\[\tan(60) = \frac{AC}{5 \sqrt{3}}~~~then~~~AC = 5 \sqrt{3} \times \tan(60)\]

and

\[\tan(30) = \frac{BC}{5\sqrt{3}}~~~~~then~~~~BC = 5\sqrt{3} \times \tan(30)\]

hope it helps

Answer 13

last step

AB = AC - BC

Answer 14

i got 20ft?

Answer 15

I think you need to check the calculations

Answer 16

ok let me check

Answer 17

ohhhhh ok so now i see what i did wrong is the answer 15?

Answer 18

well AC is 15

now calculate BC

Answer 19

so bc is 5 right?

Answer 20

yes

Answer 21

that would mean the answer is 10 right?

Answer 22

correct

Answer 23

THANK SO MUCH !!!!!!!