wanson plans to attempt to swim across the lake from point A to point B as shown below. To determine how far he will have to swim, he has chosen a point C and calculated the labeled data. How many miles will he have to swim? Round your answer to two decimal places. 8.5 10.7

Question

Spark269 · Answer

A 8.5 B 10.7 C43.5

Vocaloid · Answer

|dw:1571887719375:dw|

Vocaloid · Answer

@dude whenever you get a chance
simple law of cosines problem

dude · Answer

Like Vocaloid said you need to use the law of cosines

which is just $c^2=a^2+b^2-2ab~cos(C)$
a and b are the sides (In this case, they gave us the angles A and B [note that these are capital aka the angles, the lowercase a and b are the sides opposite])

|dw:1571888769796:dw|

c [lowercase] is the **side** opposite to the angle you are trying to find
C [capital] is the **angle** opposite to the side

Anyway based on what we were given, we can just substitute what we have into the equation I showed above

a= 3.7
b= 2.5
c = c
C= 39.4

$c^2=3.7^2+2.5^2-2(3.7)(2.5)~cos(39.4º)$

I assume you are allowed to use a calculator else this would be near impossible to do by hand but once you calculate the right side of the equation, take the square root of that to get c [As from the equation it is currently c$^2$]