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September 10th, 2017, 10:35 AM  #1 
Newbie Joined: Sep 2017 From: Europe Posts: 1 Thanks: 0  Trigonometry Homework Question
Hello, I'm given a rightangled triangle with an angle of 60 degrees, nothing else. The adjacent side is named x and the opposite side is named h. The question is 'write h in terms of x. I know that the answer will be h=(square root of 3)x, as I'm given the answers at the back of the book. However, I would like to know how to solve it. Any idea how?
Last edited by skipjack; September 10th, 2017 at 02:44 PM. 
September 10th, 2017, 01:51 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,306 Thanks: 525 
You need to use the cosine (1/2) of 60 deg.

September 10th, 2017, 05:06 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1385 
Let A denote the vertex where the 60° angle is, B denote the vertex where the right angle is, and C denote the remaining vertex of the triangle. Let D be the point such that ABCD is a rectangle and O be the point of intersection of AC and BD. By symmetry, angle ABD = 60°, so triangle ABO is equilateral and AC = 2AO = 2x. By Pythagoras, h² = AC²  AB² = 4x²  x² = 3x², so h = √3x. 
September 10th, 2017, 05:20 PM  #4 
Newbie Joined: Sep 2017 From: San Diego Posts: 5 Thanks: 0 
tan(a) = h/x solve for h, h = tan(a)*x But tan(a)=sin(a)/cos(a) so h = (sin(a)/cos(a))*x If you plug in 60 for a and fill in the steps you get h = sqrt(3)*x 
September 10th, 2017, 06:51 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1385 
How would you know the values of sin(60°) and cos(60°) (yet not tan(60°))?

September 11th, 2017, 04:26 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,575 Thanks: 931 Math Focus: Elementary mathematics and beyond 
Construct an equilateral triangle with sides equaling 1 unit. Construct an altitude that divides the triangle into to congruent rightangled triangles. Then √(1  (1/2)$^2$) = √3/2, so cos(60) = 1/2, sin(60) = √3/2 and tan(60) = √3. tan(60) = h/x = √3, h = √3x. Last edited by greg1313; September 11th, 2017 at 04:36 AM. 

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