Question

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines.

Answer 1

Given: The combination of angles and sides

To Determine: If the combinations can be used to solve the triangle using law of sines

Solution

For triangle with angles ABC, and sides a, b, and c, law of sines is given as

`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`

Any triangle with at least 2 sides and an angle or at least 2 angles and an angle whose their ratio are equivalent can be solved using the law of sines.

The following are the ratio of sides and angles that are solvable

`\begin{gathered} (a)/(sinA)=(b)/(sinB),or \\ (a)/(sinA)=(c)/(sinC),or \\ (b)/(sinB)=(c)/(sinC) \end{gathered}`

Verify for question a

`\begin{gathered} a)a,A,C \\ (a)/(sinA)=(c)/(sinC),will\text{ help solve the triangle} \end{gathered}`

Verify for question b

`\begin{gathered} b)B,a,c \\ (b)/(sinB)=(a)/(sinA) \\ (b)/(sinB)=(c)/(sinC) \\ (a)/(sinA)=(c)/(sinC) \\ Non\text{ of the above cannot solve the triangle} \end{gathered}`

Answer Summary

a) a, A, C, will help solve the triangle

The correct option is (A) YES

b) B, a, c, is not sufficient to solve the triangle

The correct option is (B) NO