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CBSE Class 11-science Answered

Acute angle between the medians drawnfrom the acute angles of the right angled isosceles triangle is

 

Asked by shuvankarpaul78 | 21 Dec, 2020, 06:36: PM
Expert Answer
Let OAB be an isosceles right angled triangle right angle at O.
O is the origin, A is on x-axis and B is on y-axis.
Let OA = a and OB = b i.e. A is (a, 0) and B is (0, b)
Consider C and D as the midpoints of OB and OA respectively.
So, AC and BD are medians drawn from acute angles.
Now, the coordinates of C and D are (0, b/2) and (a/2, 0)
Slope of AC = -1/2 and slope of BD = -2
Let theta be the ngle between AC and BD, we have

tanθ equals open vertical bar fraction numerator negative begin display style 1 half end style plus 2 over denominator 1 plus open parentheses negative 2 close parentheses cross times open parentheses negative begin display style 1 half end style close parentheses end fraction close vertical bar equals open vertical bar fraction numerator begin display style 3 over 2 end style over denominator 2 end fraction close vertical bar equals 3 over 4
rightwards double arrow cosθ equals fraction numerator 4 over denominator square root of 3 squared plus 4 squared end root end fraction equals 4 over 5
rightwards double arrow straight theta equals cos to the power of negative 1 end exponent open parentheses 4 over 5 close parentheses
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