8.4 - Law of Cosines Find the missing angle x
1 answer:
Answer:
Nope, don't need to repost!
Okay, I can provide guidelines, but not the full answer.
This is the Law of Cosines: [First Attachment]
It says that the angle opposite side of the angle 77 squared is equal to... all of that, where 7 and 9 are a and b, and C is 77.
Plug in those, solve, and then you got the missing side.
Then use that in the Law of Sines: [Second Attachment], where the side opposite to an angle divided by that angle in sine is equal to the length of another side divided by its opposite angle in sine.
Essentially, plug in length 9, and divide it by sine of x, and plug in the length of missing side that we just found, and divide it by the sine of 77.
And just solve for x!
Remember to switch your calculator to degrees. Sorry that I can't solve it fully.
This is very complicated, so you can search the internet for more help if you need it.
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Answer:
10cm
Step-by-step explanation:
First let's define variables a and x:
a = area of rectangle and square
x = side of square
Now let's create an equation to calculate a using the square and an equation to calculate a using the rectangle:
Using square:
Using rectangle:
Now we want to solve for x so let's combine the equations since they are both equivalent to a
Simplify
Solving this we get 10 and -3
Since it is impossible for a square to have a negative side value we can conclude that the value is 10cm
This can then be checked by plugging in 10 as x in our equations and seeing if we get the same a value:
Using square:
Using rectangle: