Question

In ΔABCif ab=√3+√2−1/√3−√2+1and C=60°then angle A is​

Answer 1

Answer:

`c = sqrt(6), angleA = 45^(@)` and `angleA = 45^(@)`

Solution :

Given that , <br>`a=1+sqrt(3)b=2 and angle C=60^(@)` <br> We have, `c^(2)=a^(2)+b^(2)-2ab cos C` <br> `rArr c^(2)=(1+sqrt(3))^(2)+4-2(1+sqrt(3))*2 cos 60^(@)` <br>`rArr c^(2)=1+2sqrt(3)+3+4-2-2sqrt(3)` <br> `rArr c^(2)-6` <br> `rArr c= sqrt(6)` <br> Using sin rule, <br> `(a)/(sinA)=(b)/(sinB)=(c)/(sinC)` <br> `rArr (1+sqrt(3))/(sinA)=(2)/(sinB)=(sqrt(6))/(sin 60^(@))` <br> `:. sin B=(2 sin 60^(@))/(sqrt(6))=(2xx(sqrt(3))/(2))/(sqrt(6))=(1)/(sqrt(2))` <br> `rArr =B=45^(@)` <br> ` :. A=180^(@)-(60^(@)+45^(@))=75^(@)`

Step-by-step explanation:

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