Question

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

Answer 1

Answer:

$\large \boxed{\text{1204.7 in}}$

Explanation:

We can use the Law of Sines

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