Question

How far apart are the ships after 4 hours ?

Answer 1

First, lets write the angles in decimal form:

`\begin{gathered} 23\degree40^(\prime)=23+(40)/(60)=23.667 \\ 66\degree20^(\prime)=66+(20)/(60)=66.333 \end{gathered}`

Now, notice that the sum of these two angles gives us a right angle:

`23.667+66.333=90`

Next, we have to find out how many miles they traveled after the 4 hours, then, we have the following:

`\begin{gathered} (29.1)(4)=116.4 \\ (12.8)(4)=51.2 \end{gathered}`

therefore, the triangle of the picture is a right triangle with the following meausres:

using the pythagorean theorem, we get the following:

`\begin{gathered} c^2=(116.4)^2+(51.2)^2=13548.96+2621.44 \\ \Rightarrow c^2=16170.4 \\ \Rightarrow c=\sqrt[]{16170.4}=127.2 \end{gathered}`

therefore, after 4 hours, the boats are 127.2 miles apart