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
    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