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:

(pic in replies)

Angle ADC measures 45°, and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?

3.66 feet
13.66 feet
8.66 feet
5 feet

Answer 1

@AZ

Answer 2

So let's look at it one triangle at a time

Answer 3

okie

Answer 4

So now, let's just focus on the small 30-60-90 triangle



Do you know the side ratios of a 30-60-90 triangle?

Answer 5

uhhh i do not believe so

Answer 6

The ratios would be x, \( x\sqrt{3}\) and 2x

for the sides opposite 30, 60 and 90 respectively

Answer 7

so if the side opposite 60 degrees is \( 5 \sqrt{3}\)

what would the side opposite 30 degrees be?

Answer 8

remember the ratio

if the side opposite 60 degrees is \( x\sqrt{3}\)

then the side opposite 30 degrees is \( x\)

Answer 9

im sorry this is just extremely confusing. im not getting it.

Answer 10

When you have angles such as 30-60-90

or 45-45-90

then you have the sides in a certain ratio

Answer 11

what is the ratio tho...

Answer 12

im sorry none of this is making sense...

Answer 13

WAIT HOLD ON

Answer 14

Okay so like idk how i got this, but is it A?

Answer 15

You got it!