Question

rounded to the nearest tenth, what is the length of ln?
sin(20^circ) = \frac{ln}{8}
(8) sin(20^circ) = ln
\boxed{} = ln

Explanation:

Step1: Identify the formula

We are given that \(\sin(20^{\circ})=\frac{LN}{8}\) (from the problem statement, likely a right triangle with hypotenuse \(LM = 8\) and angle \(20^{\circ}\) at \(M\), so the opposite side to \(20^{\circ}\) is \(LN\)).

Step2: Solve for \(LN\)

To find \(LN\), we can rearrange the formula \(\sin(20^{\circ})=\frac{LN}{8}\) to \(LN = 8\times\sin(20^{\circ})\).
We know that \(\sin(20^{\circ})\approx0.3420\) (using a calculator for the sine of \(20\) degrees).
Then \(LN = 8\times0.3420 = 2.736\).

Step3: Round to the nearest tenth

Rounding \(2.736\) to the nearest tenth gives \(2.7\).

Answer:

\(2.7\)