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?

461.9 ft

530.9 ft

646.4 ft

325.5 ft

Answer 1

@melody16 (hehe hi again :P) this one i just need help. i dont understand much of it

Answer 2

Have you learned about special right triangles?

Answer 3

30 60 90
45 45 45
those?

Answer 4

yes, so the big triangle is a 30 60 90 triangle. and you know the length of one of the sides. How do you think you can use that information to find the length of the other side?

Answer 5

the larger angle is the 90 and the smaller unmarked angle is the 60?

Answer 6

the top one is 60 because ever triangle is 180 degrees and we know two angles. That's how you know it's 60.

Answer 7

every*

Answer 8

so we know the big triangle. How do we solve the problem with that info?

Answer 9

what do you know about a 30 60 90 triangle?

Answer 10

its a right triangle? are the leg lengths the same? and the hypotenuse different?

Answer 11

@melody16

Answer 12

Ok, the hypotenuse is twice the shortest leg. the side opposite of the 60 is whatever the other length√3 so the bottom leg is 400√3 but that is the whole thing. We need a piece of that, so we need to do the same for the smaller 30 60 90 triangle. try and see if you can do that by youself

Answer 13

would we take the 400 thats the side opposite of the 60 in the smaller triangle in this case? and divide it by the squareroot of 3?

Answer 14

@amistre64 can you help with this by chance? he had to go and im stuck now

Answer 15

i see they were dealing with special triangle proportions. my first thought was tangents

Answer 16

tan(60) = 400/x

tan(30) = 400/(x+y)

solve for y

Answer 17

tan(30) = 400/(x+y)
divide each side 30?
tan=13.33(x+y)
?
i think i did it wrong

Answer 18

tan(30) is a single value ... divide each side by tan(30)

Answer 19

tan(60) = 400/x

x = 400/tan(60)
-----------------------

tan(30) = 400/(x+y)

x+y = 400/tan(30)

y = 400/tan(30) - x .... but x=400/tan(60)

y = 400/tan(30) - 400/tan(60)

Answer 20

so i would take the opposite and adjacent sides of 30 and 60 in the big or small triangle?

Answer 21

which method are you more comfortable with, working the trig functions, or playing with special triangles?

Answer 22

i think trig would be easier

Answer 23

me too, which is why i just walked thru the trig.

the next thing to do is simply use a calculator to work it.

Answer 24

y = 400/tan(30) - 400/tan(60) that calculator knows how to work it form there :) unless you know the values for the trig functions.

Answer 25

its giving me a really small decimal when i try dividing 400 by tan 30 it does it before i even put 30 in. should i grab my scientific calc?

Answer 26

you should yes, or use the wolf.

http://www.wolframalpha.com/input/?i=400%2Ftan%2830%29+-+400%2Ftan%2860%29

Answer 27

Oh! ill make sure to save that as a favorite! and thank you for all the help i really am grateful.

Answer 28

good luck :)