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

Answer:

The given triangle is possible.

Step-by-step explanation:

Given, the measurement of triangle ABC are,

∠ B = 153°, c = 10, b = 14,

By the law of sine,

$\frac{sin C}{c}=\frac{sin B}{b}$

By cross multiplication,

$sin C = \frac{c\times sin B}{b}$  

By substituting the values,

$sin C=\frac{10\times sin 153^{\circ}}{14}$

$sin C=0.324278928386$

$\implies \angle C=18.9218948147\approx 18.922^{\circ}$

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

Hence, the given triangle is possible.

Answer 2

Answer:

C = 18.9°, A = 8.1°, a ≈ 4.3