Results 1 to 6 of 6

Math Help - Dreaded Word Problems

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    47

    Dreaded Word Problems

    So I was doing my homework quite merrily until I go to the end where I ran into word problems.. (why do they always stick them at the end)

    Can you guys point me into the right direction?

    Q#1.

    The minute hand on a clock is 6 cm long and the hour hand is 4 cm long. Give an expression for d , the distance between the tips of the hands, in terms of a , the angle between the hands.

    What Does "d"=?

    My Plan of Attack: I drew a lame picture of the clock hands neatly labeled. I noticed you can form a triangle and thus use Pythagorean to find the distance between the 2 points. But Im not sure which side is the longer side? Do you guys think it should be 6^2+4^2=c^2?

    2nd, I think, once I know the 3 side lengths, I can use either Cosine law or Sine law to find the angle..


    And what is the question asking when they are asking for an expression for "d"?

    Q#2.

    At noon, ship A passes 8 km west of a harbour, heading due south at 10 km/h. At 9 a.m., ship B had left the harbour, sailing due south at 5 km/h. Give an expression for d , the distance between the two ships, in terms of t , the number of hours after noon.

    My Plan of Attack: Confused.



    I have no idea why I can't handle word problems.




    TIA as always
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by mvho View Post
    So I was doing my homework quite merrily until I go to the end where I ran into word problems.. (why do they always stick them at the end)

    Can you guys point me into the right direction?

    Q#1.

    The minute hand on a clock is 6 cm long and the hour hand is 4 cm long. Give an expression for d , the distance between the tips of the hands, in terms of a , the angle between the hands.

    What Does "d"=?

    My Plan of Attack: I drew a lame picture of the clock hands neatly labeled. I noticed you can form a triangle and thus use Pythagorean to find the distance between the 2 points. But Im not sure which side is the longer side? Do you guys think it should be 6^2+4^2=c^2?

    2nd, I think, once I know the 3 side lengths, I can use either Cosine law or Sine law to find the angle..


    And what is the question asking when they are asking for an expression for "d"?
    Join the tips of the minute hand and hour hand,
    You have a triangle: 1 side is 6cm long, second side is 4cm long and third side is d cm.
    Since you know the angle between the known sides:Apply cosine law.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    47
    Yes, That is what I thought but I was more confused at what they actually want me to find?

    And does it matter if the unknown side is the longer side or shorter side? I am not clear about that as well.

    Do you guys think it should be 6^2+4^2=c^2 OR, c^2+4^2=6^2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by mvho View Post

    Q#2.

    At noon, ship A passes 8 km west of a harbour, heading due south at 10 km/h. At 9 a.m., ship B had left the harbour, sailing due south at 5 km/h. Give an expression for d , the distance between the two ships, in terms of t , the number of hours after noon.
    See figure.

    Ship A started from A at noon. After time t, it is at C
    hence, AC=10t

    Ship B started at harbour(B) at 9am. At noon, it was at D.
    BD=????
    At time t after noon, it is at E.
    DE=????
    Attached Thumbnails Attached Thumbnails Dreaded Word Problems-ship.bmp  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    May 2009
    Posts
    527
    Quote Originally Posted by mvho View Post
    Yes, That is what I thought but I was more confused at what they actually want me to find?

    And does it matter if the unknown side is the longer side or shorter side? I am not clear about that as well.

    Do you guys think it should be 6^2+4^2=c^2 OR, c^2+4^2=6^2?
    Neither! You only use the Pythagorean Theorem for right triangles, and for the most part, the triangles formed by the two hands plus the distance between them at the tips are not right triangles. You have a triangle where you know two of the sides, and the angle between them is a. The unknown side is d. As malaygoel said, just use the Law of Cosines:

    \begin{aligned}<br />
d^2 &= 4^2 + 6^2 - 2(4)(6)\cos a \\<br />
d^2 &= 52 - 48\cos a \\<br />
d &= \sqrt{52 - 48\cos a}<br />
\end{aligned}

    See diagram below.


    01
    Attached Thumbnails Attached Thumbnails Dreaded Word Problems-clock-lawofcosines.jpg  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    May 2009
    Posts
    47
    Thanks everyone

    Ship A started from A at noon. After time t, it is at C
    hence, AC=10t

    Ship B started at harbour(B) at 9am. At noon, it was at D.
    BD=????
    At time t after noon, it is at E.
    DE=????
    So, BD=5t
    and AC=10t

    Is it also true that the length from point A to point B is 8km since the question said it passes 8k west? If this is the case, I can use pythagorean since a rectangle would be a right triangle.

    I think I should have:

    d=\sqrt{8^2+5t^2}

    Since I know that AC=5t and BD=5t so if I minus 10t-5t, I'll know the length.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problems with integration word problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2010, 06:39 PM
  2. Dreaded identities and double angle formulae
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 25th 2009, 08:35 AM
  3. Word problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 30th 2008, 04:58 PM
  4. More of those dreaded circles
    Posted in the Geometry Forum
    Replies: 4
    Last Post: December 29th 2007, 09:23 AM
  5. Word problems
    Posted in the Math Topics Forum
    Replies: 9
    Last Post: October 8th 2006, 09:26 PM

Search Tags


/mathhelpforum @mathhelpforum