Question

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

A = 59°, a = 13, b = 14

help me please

Answer 1

Answer on question 42447 – Math - Geometry

Question:

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

$A = 59{}^{\circ}, a = 13, b = 14$

Solution:

According to the Law of Sines we get

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

Or

$$\frac{13}{\sin 59{}^{\circ}} = \frac{14}{\sin B} = \frac{c}{\sin C}$$ $$\frac{13}{\sin 59{}^{\circ}} \approx 15.2,$$ $$\frac{14}{\sin B} \approx 15.2 \Rightarrow \sin B = 0.9 \Rightarrow B \approx 67{}^{\circ} \text{ or } B \approx 113{}^{\circ}$$

As we know $A + B + C = 180{}^{\circ}$ that is why $C = 180{}^{\circ} - 59{}^{\circ} - 67{}^{\circ} = 54{}^{\circ}$ or $C = 8{}^{\circ}$.

And

$$\frac{c}{\sin 54{}^{\circ}} \approx 15.2 \Rightarrow c \approx 12.3 \text{ or } \frac{c}{\sin 8{}^{\circ}} \approx 15.2 \Rightarrow c \approx 2.$$

Answer: 1) $A = 59{}^{\circ}, B = 67{}^{\circ}, C = 54{}^{\circ}, a = 13, b = 14, c = 12.3$.

2) $A = 59{}^{\circ}, B = 113{}^{\circ}, C = 8{}^{\circ}, a = 13, b = 14, c = 2$.

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