Topic: Math question: find height from distance and two angles

[alanjt]

I'm totally blanking on how to find the height and I can't find the solution on line. Could someone much smarter than I am please tell me how?

I have two angles: 90°53'36" and 85°26'05", with a distance of 205.12'.

Thanks, guys.

[paulmcz]

I am not sure I understand your problem correctly but if that is a triangle with two angles and a side between them, this should work.

Code: [Select]

(defun dtr (x)
(* pi (/ x 180.000)))

(defun tan (xx)
(/ (sin xx)(cos xx)))

(setq a (- pi (dtr 90.8933333333))
      b (dtr 85.434722222)
      d 205.12
      h (/ (* (tan b) d (tan a))(- (tan a)(tan b))))

[Kerry]

Alan, We want pictures ! 

[diarmuid]

Not being crazy but, given the information, could you not just draw the triangle in AutoCAD and then measure from it?

[Rob...]

That's what I would have done but was thinking the OP wanted the mathematical solution.

[alanjt]

Yes, I could have just done it in cad, but I couldn't remember the formula and that's what I was looking for.

BTW, thank you, Paul.

[CAB]

Alan,
Do you have Terry's routine?

Code: [Select]

;|
Here is  a TRI  function that  I wrote  last year  for calculating the sides and
angles of right and oblique triangles.  The function is fairly easy to  use.  It
has six arguments:  Side s1, Side  s2, Side s3,  Angle a, Angle  b, and Angle c.
Angles are  in radians.   It returns  a 1  based list  so you  can use the ‘nth’
function to retrieve your results.   To display the text help  information, just
type (tri ? ? ? ? ? ?) on the command line as follows:
Note: This displays better using a courier or mono-spaced font.
Command: (tri ? ? ? ? ? ?)
tri error: (tri nil nil nil nil nil nil)
Only 2 or 3 valid arguments can be passed to tri function.
tri - Calculates the sides and angles of a triangle
Arguments: 6             |\                /\
  s1 = Side s1           |a\              /a \
  s2 = Side s2           |  \            /    \
  s3 = Side s3        s2 |   \ s3    s2 /      \ s3
  a = Angle a radians    |    \        /        \
  b = Angle b radians    |c___b\      /c________b\
  c = Angle c radians      s1              s1
Syntax example: (tri 3 ? ? 0.643501 ? ?);where ? = nil
Returns: (list nil 3.0 4.0 5.0 0.643501 0.927295 1.5708)
Note: For right triangles only supply the argument values for 2 sides,
or 1 side and 1 angle. Use ? or nil for the Angle c argument value.
For oblique triangles only supply argument values for 3 sides,
or 2 sides and 1 angle, or 1 side and 2 angles.
|;

;-------------------------------------------------------------------------------
; tri - Calculates the sides and angles of a triangle
; Arguments: 6             |                 /\
;   s1 = Side s1           |\               /a \
;   s2 = Side s2           |a\             /    \
;   s3 = Side s3        s2 |  \ s3     s2 /      \ s3
;   a = Angle a radians    |   \         /        \
;   b = Angle b radians    |c__b\       /c________b\
;   c = Angle c radians      s1              s1
; Syntax example: (tri 3 ? ? 0.643501 ? ?);where ? = nil
; Returns: (list nil 3.0 4.0 5.0 0.643501 0.927295 1.5708);nth 1 based list
; Note: For right triangles only supply the argument values for 2 sides, or
; 1 side and 1 angle. Use ? or nil for the Angle c argument value. For oblique
; triangles only supply argument values for 3 sides, or 2 sides and 1 angle,
; or 1 side and 2 angles.
; Programming example usages:
; (setq Side2 (nth 2 (tri 3 ? ? 0.643501 ? ?))) = 4.0
; (setq AngleB (nth 5 (tri 3 ? ? 0.643501 ? ?))) = 0.927295

[alanjt]

Alan,
Do you have Terry's routine?

Code: [Select]

;|
Here is  a TRI  function that  I wrote  last year  for calculating the sides and
angles of right and oblique triangles.  The function is fairly easy to  use.  It
has six arguments:  Side s1, Side  s2, Side s3,  Angle a, Angle  b, and Angle c.
Angles are  in radians.   It returns  a 1  based list  so you  can use the ‘nth’
function to retrieve your results.   To display the text help  information, just
type (tri ? ? ? ? ? ?) on the command line as follows:
Note: This displays better using a courier or mono-spaced font.
Command: (tri ? ? ? ? ? ?)
tri error: (tri nil nil nil nil nil nil)
Only 2 or 3 valid arguments can be passed to tri function.
tri - Calculates the sides and angles of a triangle
Arguments: 6             |\                /\
  s1 = Side s1           |a\              /a \
  s2 = Side s2           |  \            /    \
  s3 = Side s3        s2 |   \ s3    s2 /      \ s3
  a = Angle a radians    |    \        /        \
  b = Angle b radians    |c___b\      /c________b\
  c = Angle c radians      s1              s1
Syntax example: (tri 3 ? ? 0.643501 ? ?);where ? = nil
Returns: (list nil 3.0 4.0 5.0 0.643501 0.927295 1.5708)
Note: For right triangles only supply the argument values for 2 sides,
or 1 side and 1 angle. Use ? or nil for the Angle c argument value.
For oblique triangles only supply argument values for 3 sides,
or 2 sides and 1 angle, or 1 side and 2 angles.
|;

;-------------------------------------------------------------------------------
; tri - Calculates the sides and angles of a triangle
; Arguments: 6             |                 /\
;   s1 = Side s1           |\               /a \
;   s2 = Side s2           |a\             /    \
;   s3 = Side s3        s2 |  \ s3     s2 /      \ s3
;   a = Angle a radians    |   \         /        \
;   b = Angle b radians    |c__b\       /c________b\
;   c = Angle c radians      s1              s1
; Syntax example: (tri 3 ? ? 0.643501 ? ?);where ? = nil
; Returns: (list nil 3.0 4.0 5.0 0.643501 0.927295 1.5708);nth 1 based list
; Note: For right triangles only supply the argument values for 2 sides, or
; 1 side and 1 angle. Use ? or nil for the Angle c argument value. For oblique
; triangles only supply argument values for 3 sides, or 2 sides and 1 angle,
; or 1 side and 2 angles.
; Programming example usages:
; (setq Side2 (nth 2 (tri 3 ? ? 0.643501 ? ?))) = 4.0
; (setq AngleB (nth 5 (tri 3 ? ? 0.643501 ? ?))) = 0.927295

I do not, but that looks rather impressive.

[ribarm]

Alan, in case you didn't google it, here is link :

http://www.theswamp.org/index.php?topic=15698.msg191722#msg191722

[paulmcz]

Yes, I could have just done it in cad, but I couldn't remember the formula and that's what I was looking for.

BTW, thank you, Paul.

You are welcome.
Here is how I came to the formula (attached). No Google.

[CAB]

Thanks for the link, I was missing that. 

Alan, in case you didn't google it, here is link :

http://www.theswamp.org/index.php?topic=15698.msg191722#msg191722

[MeasureUp]

I am not sure I understand your problem correctly but if that is a triangle with two angles and a side between them, this should work.

Code: [Select]

(defun dtr (x)
(* pi (/ x 180.000)))

(defun tan (xx)
(/ (sin xx)(cos xx)))

(setq a (- pi (dtr 90.8933333333))
      b (dtr 85.434722222)
      d 205.12
      h (/ (* (tan b) d (tan a))(- (tan a)(tan b))))

Sorry, I think the height in your code should be:
(setq h (/ (* (tan b) d (tan a)) (+ (tan a) (tan b))))

[paulmcz]

I disagree

[MeasureUp]

I disagree

Have you tried what Alan given and drawn it in AutoCAD?
Angle 1 = 90.8933333333 deg
Angle 2 = 85.434722222 deg
Distance = 205.12
What would you get for the height?
Would it be the same as what you calculated from your code?
Thanks.

[paulmcz]

Yes, I did draw it and measured to verify my code result. See the attached drawing in my second post here.