Question

rounded to the nearest tenth, what is the length of ln? sin(20°) = ln/8 (8)sin(20°) = ln = ln

Explanation:

Step1: Recall sine - ratio formula

In right - triangle \(LMN\) with right - angle at \(N\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 20^{\circ}\), the hypotenuse \(LM = 8\) and the side opposite to the angle \(20^{\circ}\) is \(LN\). So, \(\sin(20^{\circ})=\frac{LN}{8}\).

Step2: Solve for \(LN\)

Multiply both sides of the equation \(\sin(20^{\circ})=\frac{LN}{8}\) by 8. We get \(LN = 8\times\sin(20^{\circ})\).
We know that \(\sin(20^{\circ})\approx0.342\). Then \(LN=8\times0.342 = 2.736\).

Step3: Round to the nearest tenth

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

Answer:

\(2.7\)