Question

hi! i need help with this question asap (to be solved and drawn out) i know that it is using law of cosines but need more help on how to apply it:) thank you! - There is secret treasure hidden in the woods. Kevin and Randall are both on a secret treasure hunt on a mission to find it and if they follow their clues carefully, they will cross paths and find the treasure. After finding 3 clues, they end up facing each other 10 meters apart. Kevin finds a clue that says to turn a little towards the north and to walk 55 meters to find the treasure. Randall finds a clue that says to walk 60 meters to find the treasure. How many degrees should Randall turn towards the north?

Answer 1

In a diagram,

There are multiple possible diagrams, this is just one of them.

To find the angle θ using the cosine law, proceed as shown below

`\begin{gathered} c^2=a^2+b^2-2ab\cos \theta \\ c\to\text{opposite side to }\theta \end{gathered}`

Solving the equation for θ

`\begin{gathered} \Rightarrow c^2-a^2-b^2=-2ab\cos \theta \\ \Rightarrow(a^2+b^2-c^2)/(2ab)=\cos \theta \\ \Rightarrow\theta=\cos ^(-1)((a^2+b^2-c^2)/(2ab)) \end{gathered}`

In our case,

`c=55,a=60,b=10`

Thus,

`\begin{gathered} \Rightarrow\theta=\cos ^(-1)((675)/(1200))=\cos ^(-1)((9)/(16))=55.77dgr \\ \Rightarrow\theta=55.77\text{dgr} \end{gathered}`

The answer is 55.77°