Question

The 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. B = 153°, c = 10, b = 14

Answer 1

C = 18.9°, A = 8.1°, a ≈ 4.3

Answer 2

The given triangle is possible.

Explanation:

Given, the measurement of triangle ABC are,

∠ B = 153°, c = 10, b = 14,

By the law of sine,

`(sin C)/(c)=(sin B)/(b)`

By cross multiplication,

`sin C = (c* sin B)/(b)`

By substituting the values,

`sin C=(10* sin 153^(\circ))/(14)`

`sin C=0.324278928386`

`\implies \angle C=18.9218948147\approx 18.922^(\circ)`

Since, with help of sin law we found the measurement of the unknown angle of the triangle.

Hence, the given triangle is possible.