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 1

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_Seg_One_Exam_33/image0014e3941ae.jpg

Answer 2

Do you know how to solve 30-60-90 triangles?
The sides are in this ratio: short side = 1, hypotenuse = 2, third side = sqrt(3)

Answer 3

yeah

Answer 4

So you can tell me what BC is?

Answer 5

\[\tan(60) = \frac{100}{BC}\]

Find BC from here..

Answer 6

BC=57.7 right?

Answer 7

In that triangle, BC is to 100 as 1 is to sqrt(3)

Answer 8

????

Answer 9

Yes

Answer 10

ok

Answer 11

You can do it other way also:

\[\tan(60) = \sqrt{3}\]

Answer 12

@Sunshine447 do you know about sines and cosines?

Answer 13

yeah

Answer 14

For 30-60-90 I prefer not to get into that, just remember the basic ratio 1-2-sqrt(3)

Answer 15

ok

Answer 16

\[BC = \frac{100}{\sqrt{3}} \implies \frac{100 \sqrt{3}}{3}\]

Now find:

\[\tan(30) = \frac{100}{BD}\]

Answer 17

\[\tan(30) = \frac{\sqrt{3}}{3}\]

Answer 18

Now, you can get BD because that triangle is also 30-60-90

Answer 19

Then just do:

\(BD - BC\)

You will get \(CD\)..

Answer 20

115.5?

Answer 21

Let me check..

Answer 22

sqrt(3) 100 - 100/sqrt(3)

Answer 23

I got

>>> a = 3**0.5
>>> 1.0/a
0.5773502691896258
>>> a*100 - 1.0/a
172.6277304876981

Answer 24

\[BD = \frac{300}{\sqrt{3}} \implies \frac{300 \sqrt{3}}{3}\]

Answer 25

oops

>>> a*100 - 100.0/a
115.47005383792515
>>>

we match

Answer 26

yay! thanks guys!

Answer 27

yw

Answer 28

\[BD - BC = \frac{200 \sqrt{3}}{3} \implies CD = 115.48 \approx \color{green}{115.5}\]