Question

1. find ab
2. find m∠c
3. find m∠a

Explanation:

11) Find \( AB \)

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( c^{2}=a^{2}+b^{2}-2ab\cos C \). Here, \( a = 13 \), \( b = 20 \), \( C=93^{\circ} \), and \( c = AB \).

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Step2: Take the square - root

\( AB=\sqrt{596.196}\approx24.4 \) in.

13) Find \( m\angle C \)

Step1: Apply the Law of Cosines

The Law of Cosines formula \( \cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab} \). Here, \( a = 14.5 \), \( b = 13.7 \), \( c \) is the side opposite \( \angle C \). First, find the side opposite \( \angle C \) using the Law of Cosines:

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\( AC=\sqrt{449.81}\approx21.2 \) in.
Then, \( \cos C=\frac{13.7^{2}+21.2^{2}-14.5^{2}}{2\times13.7\times21.2} \)

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15) Find \( m\angle A \)

Step1: Apply the Law of Cosines

The Law of Cosines formula \( \cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc} \). Here, \( a = 16 \), \( b = 28 \), \( c \) is the side opposite \( \angle A \). First, find the side opposite \( \angle A \) using the Law of Cosines:

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\( AB=\sqrt{1447.78}\approx38.18 \) mi.
Then, \( \cos A=\frac{16^{2}+38.18^{2}-28^{2}}{2\times16\times38.18} \)

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Answer:

1. \( AB\approx24.4 \) in.
2. \( m\angle C\approx42.6^{\circ} \)
3. \( m\angle A\approx40.5^{\circ} \)