Results 1 to 2 of 2

Math Help - 3D question

  1. #1
    Senior Member
    Joined
    Jul 2009
    From
    Singapore
    Posts
    338

    3D question

    A pole, base at O, is on the west bank of a river. Two points, A and B, stand on the east bank of the river whose banks run parallel north to south. A to the south of O and B to the north. the distance AB is [tex]2a\sqrt{7}[/math and the angle AOB is 150^o. If the angle of elevation of the top of the pole, P, from A is 45^o and 30^o from B, find in terms of a the height of the pole and the width of the river.

    I know OP=OA and OA= 4a\sqrt{7}\sin B
    and (A+B)=30^o but i don't know how to eliminate the sinB
    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    Quote Originally Posted by arze View Post

    I know OP=OA and OA= 4a\sqrt{7}\sin B
    and (A+B)=30^o but i don't know how to eliminate the sinB
    thanks
    OB = 4a\sqrt{7}\sin A = sqrt{3}OP
    OA= 4a\sqrt{7}\sin B = OP
    Sin(A)/sin(B) = sqrt{3}. But A = (30 - B)
    So sin(30 - B)/sin(B) = sqrt{3}. expand sin(30-B)
    (sin30*cos(B) - cos30*sinB)/sin(B) = sqrt{3}
    1/2*cot(B) - sqrt{3}/2 = sqrt{3}
    Solve the equation and find the angle B.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum