Angles of Elevation and Depression

[keri__lynn]

Here is my question

it says Two boats are observed by a parasailer 75 meters above a lake. The angles of depression are 12.5 degrees and 7 degrees. How far apart are the boats?


Here is an example i have to go by i did work this problem out like this example but i got the wrong answer... can you please show me how to work this problem out step by step....

The example given is indrect measurement

Olivia is in a lighthouse on a cliff. She observes two sailboats due east of the lighthouse. The angles of depression to the two boats are 33 degrees and 57 degrees. Find the distance between the two sailboats to the nearest foot.

triangle CDA and CDB are right triangles and CD = 110 + 85 or 195. The distance between the boats is AB or BD - AD. Use the right traingles to find these two lenths.

Because CE and DB are horizontal lines, they are parallel. Thus <ECB = <CBD and <ECA = <CAD because they are alternate interior angles. This means that m<CBD = 33 and m<CAD = 57.

tan 33 degrees = 195 / DB

DB tan 33 = 195

DB = 195 / tan 33

DB = 300.27

tan 57 = 195 / DA

DA tan 57 = 195

DA = 195 / tan 57

DA = 126.63

the distance between the boats is DB - DA.

DB - DA = 300.27 - 126.63 or about 174 feet

 

[stapel]

i did work this problem out like this example but i got the wrong answer.

We already know how to work these exercises, so we don't need the worked example to "follow". And if the various worked examples in class and in your textbook haven't helped, then another worked example of the exact same sort is unlikely to improve your situation.

Please reply with a clear listing of your steps and solution, so we can "see" what you are doing. (We cannot help correct errors that we cannot see.)

Please be complete. Thank you!

Eliz.

 

[galactus]

it says Two boats are observed by a parasailer 75 meters above a lake. The angles of depression are 12.5 degrees and 7 degrees. How far apart are the boats?

There are numerous ways to set it up. You can set up two equations with two unknowns and solve. I am sorry, I did not look through your other problem yet.

It may be a little easier to use the complementary angles for the ones given.

\(\displaystyle tan(77.5)=\frac{x}{75}\)

\(\displaystyle tan(83)=\frac{x+y}{75}\)

See how I got those?. Look at the drawing.