Consider three lines as follows.$$L1$$:$$5x$$−$$y+4=0L2$$:$$3x$$−$$y+5=0L3$$:$$x+y+8=0If$$ these lines enclose a triangle ABC and sum of the square of the tangent to the angles can be expressed in the form $$p/q$$, where p and Q are relatively prime numbers, then the value of $$p+q$$ is

Question

Infinity Learn · Accepted Answer

Arranging the lines in descending order of slope, we have $$m1=5$$, $$m2=3$$, and $$m3=$$−$$1$$∴  $$tanA=m1$$−$$m21+m1m2=21+15=18tanB=m2$$−$$m31+m2m3=3+11$$−$$3=$$−$$2tanC=m3$$−$$m11+m3m1=$$−$$1$$−$$51$$−$$5=32$$∑$$tan2A=164+4+94=1+256+14464=40164or$$ $$p+q=465$$

Consider three lines as follows.
$L_{1} : 5 x - y + 4 = 0$
$L_{2} : 3 x - y + 5 = 0$
$L_{3} : x + y + 8 = 0$
If these lines enclose a triangle ABC and sum of the square of the tangent to the angles can be expressed in the form p/q, where p and Q are relatively prime numbers, then the value of p+q is

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Consider three lines as follows.L1:5x−y+4=0L2:3x−y+5=0L3:x+y+8=0If these lines enclose a triangle ABC and sum of the square of the tangent to the angles can be expressed in the form p/q, where p and Q are relatively prime numbers, then the value of p+q is

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Ready to Test Your Skills?

free study material