Question

I need help , it would also help if someone gave a step by step explication so I can do the rest by my self

Answer 1

First, let's focus in this portion:

Let's use sine identity:

`\begin{gathered} \sin (\theta)=\frac{opposite}{\text{hypotenuse}} \\ \sin (30)(w)/(8) \\ \text{Solving for w:} \\ w=8\cdot\sin (30)=4 \end{gathered}`

Now, let's focus in this portion:

Let's use tangent identity:

`\begin{gathered} \tan (\theta)=\frac{opposite}{\text{adjacent}} \\ \\ \tan (30)=(y)/(4) \\ \text{solving for y:} \\ y=4\cdot\tan (30)=\frac{4\sqrt[]{3}}{3}\approx2.309 \end{gathered}`

Let's focus on the first portion again:

AB would be:

AB= y + z

Let's find z using tangent identity:

`\begin{gathered} \tan (30)=(4)/(z) \\ \text{Solving for z:} \\ z=(4)/(\tan (30))=4\sqrt[]{3}\approx6.928 \end{gathered}`

Therefore:

`AB=\frac{4\sqrt[]{3}}{3}+4\sqrt[]{3}=\frac{16\sqrt[]{3}}{3}\approx9.2376`