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In ΔFGH, h = 980 inches, ∠H=114° and ∠F=48°. Find the length of f, to the nearest 10th of an inch.

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znk

Answer:

[tex]\large \boxed{\text{1204.7 in}}[/tex]

Explanation:

We can use the Law of Sines

[tex]\begin{array}{rcl}\dfrac{\sin H}{h} & = & \dfrac{\sin F}{f}\\\\f &= &h \times \dfrac{\sin F}{\sin H}\\\\&= & \text{980 in} \times \dfrac{\sin 114^{\circ}}{\sin 48^{\circ}}\\\\&= & \text{980 in} \times \dfrac{0.9135}{0.7341}\\\\& = &\text{980 in} \times 1.229  \\& = & \textbf{1204.7 in}\\\end{array}\\\text{The length of f is $\large \boxed{\textbf{1204.7 in}}$}[/tex]

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Cetacea

Answer: the length of f is 797.2 inches.

Given that: h = 980 inches, ∠H=114° and ∠F=48°.

We have to find f.

We will use the law of sine.

[tex]\frac{h}{\sin H}=\frac{f}{\sin F}\\\frac{980}{\sin114}=\frac{f}{\sin48}\\f=\frac{980}{\sin114}\cdot\sin48\\f=797.203820429\\f=797.2[/tex]

So the length of f is 797.2 inches.

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