Question

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer. Law of sines: answers- 1. 1.9 units 2. 4.7 units 3. 5.0 units 4. 5.7 units

Answer 1

Answer:

$\boxed{\text{2. 4.7 units}}$

Step-by-step explanation:

Assume your triangle has the dimensions shown below.

Before we can use the Law of Sines, we must find ∠C.

1. Calculate ∠C

$\begin{array}{rcl}A + B + C & = & 180^{\circ}\\66^{\circ} + 76^{\circ} + C & = & 180^{\circ}\\142^{\circ} + C & = & 180^{\circ}\\C & = & 38\, ^{\circ}\\\end{array}$

2. Calculate b

Use the Law of Sines

$\begin{array}{rcl}\dfrac{b}{\sin B } & = & \dfrac{c}{\sin C}\\\\\dfrac{b}{\sin 76^{\circ}} & = & \dfrac{3}{\sin 38^{\circ}}\\\\\dfrac{b}{0.9703} & = & \dfrac{3}{0.6157}\\\\ & = & 4.873\\b & = & 0.9703\times 4.873\\& = & \boxed{\mathbf{4.7}}\\\end{array}$