# Hypotenuse and height

#0  xxx() called at [/LinSys.php:671]
#1  LinSys::tryIntegerEquations(Array ([0] => D,[1] => F,[2] => a,[3] => b,[4] => c,[5] => d,[6] => e,[7] => f,[8] => m,[9] => o,[10] => p,[11] => r,[12] => t,[13] => x), Array ([0] => x^2 -56x +16 =0,[1] => a=1,[2] => b=-56,[3] => c=16,[4] => D = b^2 - 4ac = 56^2 - 4** 1 ** 16 = 3072,[5] => xx{1.2} = frac{ -b pm sqrt{ D } }{ 2a } = frac{ 56 pm sqrt{ 3072 } }{ 2 } = frac{ 56 pm 32 sqrt{ 3 } }{ 2 },[6] => xx{1.2} = 28 pm 27.712812921102,[7] => xx{1} = 55.712812921102,[8] => xx{2} = 0.28718707889796,[9] => (x -55.712812921102) (x -0.28718707889796) = 0), 1) called at [/LinSys.php:344]
#2  LinSys::SolveInner(x^2 -56x +16 =0
a=1; b=-56; c=16
D = b^2 - 4ac = 56^2 - 4** 1 ** 16 = 3072
D>0

xx{1.2} = frac{ -b pm sqrt{ D } }{ 2a } = frac{ 56 pm sqrt{  3072 } }{ 2 } = frac{ 56 pm 32  sqrt{ 3 } }{ 2 }
xx{1.2}  = 28 pm 27.712812921102
xx{1}  = 55.712812921102
xx{2}  = 0.28718707889796

text{ Factored form: }
(x -55.712812921102) (x -0.28718707889796) = 0, , 1, linsys, 1, , 1, 1) called at [/LinSys.php:220]
#3  LinSys::Solve(x^2 -56x +16 =0
a=1; b=-56; c=16
D = b^2 - 4ac = 56^2 - 4** 1 ** 16 = 3072
D>0

x_{1,2} = \frac{ -b \pm \sqrt{ D } }{ 2a } = \frac{ 56 \pm \sqrt{  3072 } }{ 2 } = \frac{ 56 \pm 32  \sqrt{ 3 } }{ 2 }
x_{1,2}  = 28 \pm 27.712812921102
x_{1}  = 55.712812921102
x_{2}  = 0.28718707889796

\text{ Factored form: }
(x -55.712812921102) (x -0.28718707889796) = 0, , 1, linsys, 1, , 1) called at [/Example_Generic.php:87]
#4  Example_Generic->GenerateSolveVector(stdClass Object ([example_id] => 518,[title_sk] => Prepona a výška,[title_en] => Hypotenuse and height,[title_cz] => Přepona a výška,[add_date] => 2012-12-16 02:15:15,[img] => euklides.jpg,[visible] => 1,[text_sk] => V pravouhlom trojuholníku je daná dĺžka prepony c=$c cm a výška vc=$vc cm. Určite dĺžky oboch odvesien.,[text_en] => In a right triangle is length of the hypotenuse c = $c cm and height hc =$vc cm. Determine the length of both trangle legs.,[text_cz] => V pravoúhlém trojúhelníku je dána délka přepony c=$c cm a výška vc =$vc cm. Určitě délky obou odvěsen.,[input_vector] => $c = rand(10,200);$vc = rand(1,(int)($c/2)); ,[output_vector] =>$a->in="a=#cm";
$b->in="b=#cm";$a->N = $b->N = 1;$eq = array('a','b');

$a->wolfram =$b->wolfram = "$c=x+y;$vc*$vc=xy; a^2=x*$c; b^2=y*$c; b>0 ; a>0"; list($x1, $x2) = QER(1,-$c,$vc*$vc, false);

$a->val="sqrt($x1*$c)";$b->val="sqrt($x2*$c)";

$eq = QTex(1,-$c,$vc*$vc,'x', true);

$a->tex = "$c=x+y
$vc^2=xy x($c-x) = $vc^2$eq

a = \\sqrt{ x_1 ** $c } = RES";$b->tex = "b = \\sqrt{ x_2 ** $c } = RES";,[user_id] => 12,[approved] => 1,[cnt_views] => 22905,[cnt_solved] => 2064,[cnt_solved_ok] => 31,[focus] => 1,[preview_sk] => V pravouhlom trojuholníku je daná dĺžka prepony c=32 cm a výška vc=14 cm. Určite dĺžky oboch odvesien.,[preview_en] => In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.,[preview_cz] => V pravoúhlém trojúhelníku je dána délka přepony c=56 cm a výška vc = 4 cm. Určitě délky obou odvěsen.,[preview_vector_sk] => O:8:"stdClass":2:{s:1:"c";i:32;s:2:"vc";i:14;},[preview_vector_en] => O:8:"stdClass":2:{s:1:"c";i:56;s:2:"vc";i:4;},[preview_vector_cz] => O:8:"stdClass":2:{s:1:"c";i:56;s:2:"vc";i:4;},[last_regenerate] => 2019-07-14 17:42:27,[external_url] => ,[suggestion_id] => 0,[fulltext_sk] => ~ prepona a vyska v pravouhlom trojuholniku je dana dlzka prepony c=32 cm v c =14 urcite dlzky oboch odvesien kvadraticka rovnica algebra planimetria pravouhly trojuholnik euklidove vety realne cisla stredna skola 518 ~,[fulltext_en] => ~ hypotenuse and height in a right triangle is length of the hypotenuse c = 56 cm h 4 determine both trangle legs algebra quadratic equation planimetrics the altitude theorem real numbers high school 518 ~,[fulltext_cz] => ~ prepona a vyska v pravouhlem trojuhelniku je dana delka prepony c=56 cm v c = 4 urcite delky obou odvesen algebra kvadraticka rovnice planimetrie pravouhly trojuhelnik euklidovy vety realna cisla stredni skola 518 ~,[english_last_modified] => 0000-00-00 00:00:00,[title] => Hypotenuse and height,[text] => In a right triangle is length of the hypotenuse c =$c cm and height hc = $vc cm. Determine the length of both trangle legs.), stdClass Object ([c] => 56,[vc] => 4)) called at [/Example_Generic.php:869] #5 Example_Generic->Run(stdClass Object ([example_id] => 518,[title_sk] => Prepona a výška,[title_en] => Hypotenuse and height,[title_cz] => Přepona a výška,[add_date] => 2012-12-16 02:15:15,[img] => euklides.jpg,[visible] => 1,[text_sk] => V pravouhlom trojuholníku je daná dĺžka prepony c=$c cm a výška vc=$vc cm. Určite dĺžky oboch odvesien.,[text_en] => In a right triangle is length of the hypotenuse c =$c cm and height hc = $vc cm. Determine the length of both trangle legs.,[text_cz] => V pravoúhlém trojúhelníku je dána délka přepony c=$c cm a výška vc = $vc cm. Určitě délky obou odvěsen.,[input_vector] =>$c = rand(10,200);

$vc = rand(1,(int)($c/2));
,[output_vector] => $a->in="a=#cm";$b->in="b=#cm";
$a->N =$b->N = 1;
$eq = array('a','b');$a->wolfram = $b->wolfram = "$c=x+y; $vc*$vc=xy; a^2=x*$c; b^2=y*$c; b>0 ; a>0";

list($x1,$x2) = QER(1,-$c,$vc*$vc, false);$a->val="sqrt($x1*$c)";
$b->val="sqrt($x2*$c)";$eq =  QTex(1,-$c,$vc*$vc,'x', true);$a->tex = "$c=x+y$vc^2=xy

x($c-x) =$vc^2

$eq a = \\sqrt{ x_1 **$c } = RES";

$b->tex = "b = \\sqrt{ x_2 **$c } = RES";,[user_id] => 12,[approved] => 1,[cnt_views] => 22905,[cnt_solved] => 2064,[cnt_solved_ok] => 31,[focus] => 1,[preview_sk] => V pravouhlom trojuholníku je daná dĺžka prepony c=32 cm a výška vc=14 cm. Určite dĺžky oboch odvesien.,[preview_en] => In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.,[preview_cz] => V pravoúhlém trojúhelníku je dána délka přepony c=56 cm a výška vc = 4 cm. Určitě délky obou odvěsen.,[preview_vector_sk] => O:8:"stdClass":2:{s:1:"c";i:32;s:2:"vc";i:14;},[preview_vector_en] => O:8:"stdClass":2:{s:1:"c";i:56;s:2:"vc";i:4;},[preview_vector_cz] => O:8:"stdClass":2:{s:1:"c";i:56;s:2:"vc";i:4;},[last_regenerate] => 2019-07-14 17:42:27,[external_url] => ,[suggestion_id] => 0,[fulltext_sk] => ~ prepona a vyska v pravouhlom trojuholniku je dana dlzka prepony c=32 cm v c =14 urcite dlzky oboch odvesien kvadraticka rovnica algebra planimetria pravouhly trojuholnik euklidove vety realne cisla stredna skola 518 ~,[fulltext_en] => ~ hypotenuse and height in a right triangle is length of the hypotenuse c = 56 cm h 4 determine both trangle legs algebra quadratic equation planimetrics the altitude theorem real numbers high school 518 ~,[fulltext_cz] => ~ prepona a vyska v pravouhlem trojuhelniku je dana delka prepony c=56 cm v c = 4 urcite delky obou odvesen algebra kvadraticka rovnice planimetrie pravouhly trojuhelnik euklidovy vety realna cisla stredni skola 518 ~,[english_last_modified] => 0000-00-00 00:00:00,[title] => Hypotenuse and height,[text] => In a right triangle is length of the hypotenuse c = $c cm and height hc =$vc cm. Determine the length of both trangle legs.)) called at [/index_real.php:185]
#6  HackMath->ExampleDetail() called at [/index_real.php:316]
#7  HackMath->ExampleAction() called at [/index_real.php:461]
#8  HackMath->Run() called at [/index_real.php:815]
#9  include(/index_real.php) called at [/index.php:41]