I need help solving a trigonometry math question.?

Use your imagination that this is a triangle side AB is longer than CA and the dots are a line from A to P

A

/.\ CA=6.862

/ . \ AB=40.815

/ : \ CAB= 89*31'10"

C/__ _ :_______\B

:

P

I need this answer to find gps coordinates

Find side CB and distance AP

The angle APB is a right angle (90*)

Note: this is way above my math level. If you could find the answer and provide an email so that I can double check the answer (cant do until I have an answer).

1 Answer

Relevance
  • 9 years ago
    Favorite Answer

    side b=CA=6.862

    side c=AB=40.815

    <A= CAB= 89*31'10

    <A=89° 31' 10"= 89.594444

    side a=CB=?

    .

    apply cosine law to get a or CB

    .

    2bc cos A=b^2 plus c^2-a^2

    .

    [2*6.862*40.815]*cos 89.594444= 6.862^2 plus 40.815^2 - a^2

    .

    (560..14506*0.0070782)=47.087044 plus 1665.864225 -a^2

    .

    3.9648346=1712.951269 -a^2

    .

    a^2=1712.951269-3.9648346

    .

    a=sqrt (1708.9864344)

    .

    a=41.3398891

    CB=41.3398891 answer (@_@)

    .

    .

    find height h or AP

    x=CP

    y=PB

    h=AP

    a=CB

    b=AC

    c=AB

    .

    x plus y =a

    x=a-y

    .

    use pythagorean:

    eq 1: h^2 =b^2-x^2

    .

    eq 2: y^2 plus h^2=c^2

    .

    apply the value of h^2 to eq 2:

    y^2 plus [b^2-x^2]=c^2

    .

    apply the value of x:

    y^2 plus b^2 - (a-y)^2=c^2

    .

    expand:

    y^2 plus b^2-(a^2- 2ay plus y^2)=c^2

    .

    y^2 is cancel when bracket is open, apply all equivalent values:

    .

    6.862^2- 41.3398891^2 plus (2*41.3398891y)=40.815^2

    .

    47.087044 -1708.9864308 plus 82.6797782y=1665.864225

    .

    -1661.8993868 plus 82.6797782y =1665.864225

    .

    82.6797782y=1665.864225 plus 1661.8993868

    .

    y=3327.7636118/82.6797782

    y=40.2488212

    .

    x=41.3398891-40.2488212

    x=1.0910678

    .

    h^2=b^2-x^2

    h=sqrt (6.862^2 - 1.0910678^2)

    h=sqrt (45.8966151)

    h=6.774704

    AP=6.774704 answer (@_@)

    .

    .

    check:

    y^2 plus h^2=c^2

    40.2488212^2 plus 6.774704^2=c^2

    .

    sqrt (1665.8642221)=c

    40.8149999=c

    .

    given from above:

    c=AB=40.815

    .

    .

    Edit:

    if you want the angles apply the value of x and y to hypotenuse b and c, you know what to do now, right?

    .

    .

    hope this helps (@_@)

Still have questions? Get your answers by asking now.