Question

Find the length of segment BA.


A) 163.3


B) 128.6


C) 84.7


D) 59.8

Answer 1

Answer:

D) 59.8

Step-by-step explanation:

m<B = 120 deg

Since we know the measure of an angle and the length of the opposite side, we can establish the ratio of the law of sines, so we use the law of sines to find the length of side BA.

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

$\dfrac{\sin A}{BC} = \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB}$

$\dfrac{\sin B}{AC} = \dfrac{\sin C}{AB}$

$\dfrac{\sin 120^\circ}{200} = \dfrac{\sin 15^\circ}{AB}$

$\dfrac{\sin 120^\circ}{200} = \dfrac{\sin 15^\circ}{AB}$

$(AB)\sin 120^\circ = 200 \sin 15^\circ$

$AB = \dfrac{200 \sin 15^\circ}{\sin 120^\circ}$

$AB = 59.8$