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Which of the following pieces of data do...

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle `A B C(R` being the radius of the circumcircle)? `a ,sinA ,sinB` (b) `a , b , c ,` `a ,sinB ,R` (d) `a ,sinA ,R`

A

`a, sin A, sin B`

B

`a, b, c`

C

`a, sin B, R`

D

`a, sin A, R`

Text Solution

Verified by Experts

By sine law in `Delta ABC`, we have
`(a)/(sinA) = (b)/(sin B) = (c)/(sin (pi - A - B)) = 2R`
or `(a)/(sinA) = (b)/(sin B) = (c)/(sin (A + B)) = 2R`
(1) If we know a, sin A, sin B, we can find b, c, and the value of angle A,B, C
(2) With a, b, c we can find `angleA , angle B, angle C` using the cosine law.
(3) a, sin B, R are given, so sin A, b and hence `sin (A + B)` and then C be found
(4) If we know a, sin A , R, then we can get the ratio `(b)/(sin B) " or " (c)/(sin (A + B))` only. We cannot determine the values of b, c, sin B, sin C separately. Therefore, the triangle cannot be determined uniquely in this case
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Knowledge Check

  • ABC is a right angled triangle with angle B = 90 ^@ , a=6 cm if the radius of the circumcircle is 5 cm then the area of Delta ABC is

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  • in a triangle ABC , let angle C = (pi)/(2) if r the in radius and R is the circumradius of the triangle ABC , then 2( r+R) equals

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    `a+b `
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  • In a triangle ABC , angleC = 90^o ,then the value of sinA +sinB -2sqrt2cos(A/2)cos(B/2) is:

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