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

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

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}(b)/(\sin B ) & = & (c)/(\sin C)\\\\(b)/(\sin 76^(\circ)) & = & (3)/(\sin 38^(\circ))\\\\(b)/(0.9703) & = & (3)/(0.6157)\\\\ & = & 4.873\\b & = & 0.9703* 4.873\\& = & \boxed{\mathbf{4.7}}\\\end{array}`