Test:328 QNo:5

In a triangle ABC, angle A = 36°, AB = AC = 1 and BC = x . If x = (p + √q)/2 then the ordered pair (p,q) is

8 Answers

11
virang1 Jhaveri ·

Cos A =(1 +√5)/4
So
Cos A = 1 + x2 - 1/2*1*x
Cos A = x/2
(1 +√5)/4 = x/2
x = (1 + √5)/2
p + √q = 1 + √5
p = 1
q =5

11
virang1 Jhaveri ·

Sin 36 = sin(90-54)
2Sin18Cos18 = Cos 54
2Sin18Cos18 = 4cos318 - 3cos18
2sin18 = 4 cos218 -3
2sin18 = 1-4sin218
Therefore quadratic equation
Sin 18 = √5 - 1/4
Cos 36 = 1 - 2 Sin218

Thus
Cos 36 = 1+√5/4

11
virang1 Jhaveri ·

Nishant Bhaiyya pls tell me if rite or wrong?

11
virang1 Jhaveri ·

Answer to this sir?

6
Kalyan IIT-K Beware I'm coming ·

hey cud u pls make me understand the meaning of this question....

62
Lokesh Verma ·

basically you have to find x..

once you have done that, you have to find p and q which satisfy the condition there.. by comparing of coefficients :)

6
Kalyan IIT-K Beware I'm coming ·

p n q r the coefficients of sin n cos??actually wat does p n q signify??i hav seen these variables in many ordered pair q.s.

62
Lokesh Verma ·

no they are not...

it is basically if you get cos A = 3+4√5 then p=3, q=4

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