Answer:
The boat turned 46° when it made its first turn
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
I have made an illustration to better help you understand the situation and have attached it as a photo below. As you can see the problem forms a triangle and we need to find the value of the angle x . We can use the Law of Cosine to solve for the value of x.
[tex]c^{2} = a^{2} + b^{2} - 2abcos(x)[/tex]
Now we plug in the values given and solve for x
[tex]18^{2} = 28^{2} + 25^{2} - 2(28)(25)cos(x)[/tex]
[tex]324= 784 + 625 - 1400cos(x)[/tex]
[tex]324= 1409 - 1400cos(x)[/tex] .... subtract 1409 on both sides
[tex]-1085= -1400cos(x)[/tex] .... divide by 1400 on both sides
[tex]0.775 = cos(x)[/tex].... use cos[tex]^{-1}[/tex] on both sides
[tex]cos^{-1}(0.775) = x[/tex]
[tex]39.19 = x[/tex]
Finally, we can see that the boat turned 39.19° when it made its first turn
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
