Question

question 4 of 40

in triangle abc, (m\angle a = 45^{\circ}), (m\angle b = 40^{\circ}), and (a = 7). which equation should you solve to find (b)?

a. (\frac{\sin 45^{\circ}}{7} = \frac{\sin 40^{\circ}}{b})

b. (b^2 = 7^2 - 2(7)b\cos 40^{\circ})

c. (\frac{\cos 45^{\circ}}{7} = \frac{\cos 40^{\circ}}{b})

d. (\frac{\sin 45^{\circ}}{b} = \frac{\sin 40^{\circ}}{7})

Explanation:

State the Law of Sines

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

Substitute the given values

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Answer:

• (A) \(\frac{\sin45^\circ}{7} = \frac{\sin40^\circ}{b}\) (Correct answer)
• (B) \(b^2 = 7^2 - 2(7)b\cos40^\circ\)
• (C) \(\frac{\cos45^\circ}{7} = \frac{\cos40^\circ}{b}\)
• (D) \(\frac{\sin45^\circ}{b} = \frac{\sin40^\circ}{7}\)