SOLUTION: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi apart, to be x = 28° and y = 52°, as shown in the figure Here is the ima

Algebra ->  Trigonometry-basics -> SOLUTION: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi apart, to be x = 28° and y = 52°, as shown in the figure Here is the ima      Log On


   

Question 932230: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi apart, to be x = 28° and y = 52°, as shown in the figure
Here is the image:
http://i.imgur.com/OImRqbV.png
Please explain
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Problem:


----------------------------------------------------------------------------
----------------------------------------------------------------------------

Solution:


(a)


Let P be the point where the plane is currently located. The length of AP is the same as the value of b (as shown below in the diagram)





Notice how the angle of depression corresponds to the congruent angle of elevation. Also I got the 100 degrees from the fact that 180-28-52 = 100


Use the law of sines to solve for b


b%2Fsin%2852%29=5%2Fsin%28100%29


b=sin%2852%29%2A%285%2Fsin%28100%29%29


b=4.00083544832203 Use a calculator here to get an approximate result


b+=+%224.00%22 Round to 2 decimal places


b+=+4 Drop the trailing zeros


So b is approximately 4 miles. This is the distance from point A to the plane.

--------------------------------------------------------------------------------------------------------------
(b)

Draw in the altitude or height (shown in blue)



Label it h for now.

Using trig, we know

Sine+=+opposite%2Fhypotenuse


sin%2828%29+=+h%2Fb


sin%2828%29+=+h%2F4.00083544832203 Plug in b+=+4.00083544832203


4.00083544832203%2Asin%2828%29+=+h


h+=+4.00083544832203%2Asin%2828%29


h+=+1.87827847037293 Use a calculator here.


h+=+1.88 Round to 2 decimal places


The value of h is approximately 1.88 miles.


So the elevation of the plane is approximately 1.88 miles.

------------------------------------------------------------------------------------------------------------------------

If you need more one-on-one help, email me at jim_thompson5910@hotmail.com. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).

Alternatively, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Any amount is greatly appreciated as it helps me a lot. This donation is to support free tutoring. Thank you.

Jim
------------------------------------------------------------------------------------------------------------------------