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:
Step-by-step explanation:
Since there are missing data, let's discuss some facts about regular polygons and their angles.
1) The sum of its Interior angles is given by:
2) Since it is a regular pentagon, each interior angle is congruent:
Each interior angle:
3) If we trace an outside line, the external angle will be supplemental, i.e.
4) If we trace from each diagonal one line segment, in a regular pentagon that will form 3 triangles with one-third of 108º,i.e.,36º
As we can see, the in the picture below
Congruent triangles are exactly the same, meaning they have the same side length, and thus same angles. Everything is exactly the same, as easy as it gets :)
So, you can compare the two pictures to get the informations you need:
, since it is a right angle
, as we can see on the right by comparison
. In fact, the angles of a triangle sum to
, so we have
. So,
yd, as we can see on the left by comparison.
Finally, we can compute using the Pythagorean theorem: