Results 1 to 2 of 2

Math Help - ACT Math Help

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    8

    ACT Math Help

    I'm studying for the math section of the ACT and I can't remember how to solve this problem.

    A right triangle has legs of length 25 sin theta feet and 25 cos theta feet for some angle theta that satisfies 0< theta< 90. What is the length, in feet, of the longest side of the triangle?

    F. theta
    G. 1
    H. 5
    J. 25
    K. Cannot be determined from the given information

    I know that the answer is J but I wasn't given an explanation. If someone could help me that would be great.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello 5441lk
    Quote Originally Posted by 5441lk View Post
    I'm studying for the math section of the ACT and I can't remember how to solve this problem.

    A right triangle has legs of length 25 sin theta feet and 25 cos theta feet for some angle theta that satisfies 0< theta< 90. What is the length, in feet, of the longest side of the triangle?

    F. theta
    G. 1
    H. 5
    J. 25
    K. Cannot be determined from the given information

    I know that the answer is J but I wasn't given an explanation. If someone could help me that would be great.
    If the longest side is x, using Pythagoras' Theorem:

    x^2 = (25\sin\theta)^2+(25\cos\theta)^2

    =25^2\sin^2\theta+25^2\cos^2\theta

    =25^2(\sin^2\theta+\cos^2\theta)

    =25^2 \times 1, using the well-known rule: \sin^2\theta+\cos^2\theta=1, for all values of \theta

    \Rightarrow x = 25

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: May 29th 2011, 12:57 AM
  2. Replies: 2
    Last Post: February 14th 2011, 02:31 AM
  3. Replies: 1
    Last Post: June 19th 2010, 10:05 PM
  4. Replies: 1
    Last Post: June 2nd 2010, 09:49 AM
  5. Replies: 2
    Last Post: February 15th 2010, 03:09 PM

Search Tags


/mathhelpforum @mathhelpforum