Question

find the length of side a. c = 6.1 a = 10° a = ?

Explanation:

Step1: Identify the Law of Sines

We use the Law of Sines, which states that $\frac{a}{\sin A}=\frac{c}{\sin C}$.

Step2: Substitute known values

We know $A = 10^\circ$, $c = 6.1$, and we need to find $a$. First, we confirm the Law of Sines formula: $\frac{a}{\sin 10^\circ}=\frac{6.1}{\sin 152^\circ}$.

Step3: Solve for \(a\)

Rearrange the formula to solve for \(a\): $a=\frac{6.1\times\sin 10^\circ}{\sin 152^\circ}$. Calculate $\sin 10^\circ\approx0.1736$, $\sin 152^\circ=\sin(180^\circ - 28^\circ)=\sin 28^\circ\approx0.4695$. Then $a=\frac{6.1\times0.1736}{0.4695}\approx\frac{1.05896}{0.4695}\approx2.255$.

Answer:

\(a\approx2.26\) (rounded to two decimal places)