Question

he given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. C = 38°, a = 19, c = 10

Answer 1

No, the triangle is not possible.

Explanation:

Given,

A triangle ABC in which C = 38°, a = 19, c = 10,

Where, angles are A, B and C and the sides opposite to these angles are a, b and c respectively,

By the law Sines,

`(sin A)/(a)=(sin C)/(c)`

`\implies sin A = (a sin C)/(c)`

By substituting the values,

`sin A = (19* sin 38^(\circ))/(10)`

`=1.16975680312`

`\implies A=sin^(-1)(1.16975680312)` = undefined

Hence, the triangle is not possible with the given measurement.