Question

Two boats start their journey from the same point A and travel along directions AC and AD, as shown below.

What is the distance, CD, between the boats?

Answer Choices:
461.9 ft

530.9 ft

646.4 ft

325.5 ft

Answer 1

@qweqwe123123123123111 @tible19

Answer 2

@tible19 this one

Answer 3

mkay thanks

Answer 4

youre welcome, and thanl you for helping me with all these questions. are you home schooled too?

Answer 5

for the time being

Answer 6

ohh yea me too

Answer 7

what program?

Answer 8

@qweqwe123123123123111 its this one(:

Answer 9

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

Answer 10

use properties of special right triangles

from this you can determine that
\[BC = \frac{400}{\sqrt{3}}\]
\[BD = 400 \sqrt{3}\]
so
\[CD = 400\sqrt{3} - \frac{400}{\sqrt{3}}\]

Answer 11

I got 692.8?

Answer 12

@qweqwe123123123123111 i know that the length of the hypotenuse is twice the length of the side opposite the 30 degree angle?

Answer 13

@qweqwe123123123123111 i got 461.9. is that right?

Answer 14

Yes. The "short side" or SS is 1x
The hypotenuse is 2x
And the "Long Side" or LS is sqrt(3)x

So here you have two 30-60-90 tris tucked inside each other:
ABD and ABC

You have to find the lengths of BD and BC
Then you subtract BC from BD and that tells you how far apart the boats are (CD)

Answer 15

@qweqwe123123123123111 @dumbcow is it 461.9?

Answer 16

Yup!!

I got 461.88 to 2 places, so 461.9 is good to 1 place!

Very good!! :-)

Answer 17

@qweqwe123123123123111 yay thanks! you're helping a lot!

Answer 18

Glad I can!! :-)

Unfortunately, I just remembered I put my lunch in the nuke over half an hour ago, and now it's cold again!! :-)

Not your fault, don't think I'm whining at you; I just get carried away with solving puzzles like these! :-)

So I'm reheating it now, and I'm gonna go eat it!! :-)

Answer 19

lol oops!:3 and okay enjoy your lunch!(: do you think you can help when you get back? you don't have to.