Question

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

ABC is a right triangle with measure of angle ABC equal to 90 degrees and length of AB equal to 400 feet. There is a point C on BD such that measure of angle ACB is 60 degrees and measure of angle ADC is 30 degrees.

What is the distance, CD, between the boats?

461.9 ft
530.9 ft
646.4 ft
325.5 ft

Answer 1

hey can i hget some help

Answer 2

Where is the diagram?

Answer 3

hang on http://learn.flvs.net/webdav/assessment_images/educator_geometry_v16/image0044e3941ae.jpg

Answer 4

hello?

Answer 5

there is some problem with that link. please check

Answer 6

oh

Answer 7

it shows that its 400 feet tall

Answer 8

at one end away from the right angle it it 30 degrees

Answer 9

then closer to the 90 degree angle it has an angle of 60

Answer 10

Save the image, download it, then upload it here, using the "Attach File" function

Answer 11

did it work now?

Answer 12

hello?

Answer 13

anyone there?

Answer 14

Therefore angle CAD is 30 degrees

Answer 15

ok

Answer 16

ACD is 120 degrees

Answer 17

oh yeah

Answer 18

adc is acute

Answer 19

u still here

Answer 20

Read my message

Answer 21

ok

Answer 22

i still dont get it can u run me through the steps

Answer 23

It is explained better there

Answer 24

You just have to understand SOH CAH TOA

Answer 25

Sin Cos Tan

Answer 26

so you just go 400 over tan(30)

Answer 27

then the same over 60?

Answer 28

thats not working

Answer 29

OHH i get it'

Answer 30

you gotta take 400 divided by tan of 30 degrees minus 400 divided by the tan of 60 degrees to get 461.9

Answer 31

all who cheat off this is the future ur welcome i got it right

Answer 32

You can solve this problem without trigonometry.

Since the triangles are 30-60-90 right triangles, you can use the known ratios of the lengths of the sides.
In a 30-60-90 triangle, the sides have lengths in the ratio:

\(1 : \sqrt 3 : 2\)

That is the ratio of the lengths of the

short leg : long leg : hypotenuse

In triangle ABD, AB is the short leg, and BD is the long leg, so

\(BD = \sqrt 3 AC = 400 \sqrt 3 ~ft\approx 692.8 ~ft\)

In triangle ABC, AB is the long leg, and BC is the short leg, so

\(BC = \dfrac{400~ft}{\sqrt 3} \approx 230.9~ft\)

Finally,

\(CD = BD - BC = 692.8 ~ft- 230.9 ~ft= 461.9 ~ft\)