anonymous
  • anonymous
i really need help. this is making me so lost and confused and pissed off. PLEASE
Trigonometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
please see the attachment
1 Attachment
anonymous
  • anonymous
i know that the answers im getting are wrong.
mathstudent55
  • mathstudent55
What is \( \dfrac{\pi}{6} \) in degrees?

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anonymous
  • anonymous
it doesnt say
anonymous
  • anonymous
i think it is cuz i look at examples and they show that they are in degrees
mathstudent55
  • mathstudent55
If you are dealing with angles measured in radians, it is very helpful to be able to convert to degrees. \( \pi ~radians = 180 ^{\circ} \) \( \dfrac{\pi}{6} radians = \dfrac{180^{\circ}}{6} = 30^{\circ} \)
mathstudent55
  • mathstudent55
|dw:1378014681148:dw|
anonymous
  • anonymous
i dont think its in radians though.
mathstudent55
  • mathstudent55
Since you have a right angle and a 30-degree angle, you have a 30-60-90 right triangle.
mathstudent55
  • mathstudent55
pi/6 is an anlge measure in radians. It equals 30 degrees.
anonymous
  • anonymous
ok
mathstudent55
  • mathstudent55
Since you have a 30-60-90 degree triangle, you can find the lengths of the other 2 sides by using the ratios of the lengths of the sides of 30-60-90 triangle.
anonymous
  • anonymous
so for the HY. 74.1/cos30?
mathstudent55
  • mathstudent55
|dw:1378014898429:dw|
anonymous
  • anonymous
but they already gave me one of the sides. where the one is there should be 74.1
mathstudent55
  • mathstudent55
Yes, that will also work.
anonymous
  • anonymous
ok and for the other side it would be 74.1tan30?
mathstudent55
  • mathstudent55
74.1 is x which is where sqrt(3) is.
anonymous
  • anonymous
oh yeah thats what i meant.
mathstudent55
  • mathstudent55
|dw:1378015121906:dw|
anonymous
  • anonymous
sorry ive been trying this problem out for a long time. this makes sense now.
anonymous
  • anonymous
b= 85.56 a=42.78
anonymous
  • anonymous
right?
mathstudent55
  • mathstudent55
cos 30 = 74.1/b b = 74.1/cos 30 b = 85.56 tan 30 = a/74.1 a = 74.1tan 30 a = 42.78
mathstudent55
  • mathstudent55
You are correct. Now part c.
anonymous
  • anonymous
part c? the acute angle? for that i got 90-PI/6
mathstudent55
  • mathstudent55
Since you did the problem with sin and tan, there was no need to convert to degrees, but you need to make sure your calculator is set to radians.
mathstudent55
  • mathstudent55
Your answer is correct, but it is written is a funny way. It's as if I asked what is the length of your classroom and you answered it is 2 meters + 15 ft long. The 90 part is in degrees and the pi/6 part is in radians.
anonymous
  • anonymous
oki know 90 is π/2 so do i add π/2 and π/6?
mathstudent55
  • mathstudent55
Since the problem gave you the angle is radians, you should answer in radians. \(90^{\circ} = \dfrac{\pi}{2} rad \) The third angle measures: \( \dfrac{\pi}{2} rad - \dfrac{\pi}{6} rad = ~?\)
mathstudent55
  • mathstudent55
No, don't add, subtract like you did in 90 - pi/6, only using both measures in radians as I showed above.
anonymous
  • anonymous
ok. i got 1.047
mathstudent55
  • mathstudent55
Use the fractions and subntract using a common denominator to get an exact answer.
anonymous
  • anonymous
π/3
mathstudent55
  • mathstudent55
\( \dfrac{\pi}{2} rad - \dfrac{\pi}{6} rad\) \( = \dfrac{3\pi}{3 \times 2} rad - \dfrac{\pi}{6} rad \) \( = \dfrac{2\pi}{6} rad \) \(= \dfrac{\pi}{3} rad \)
mathstudent55
  • mathstudent55
Correct.
anonymous
  • anonymous
that makes so much sense. thank you so so much.
anonymous
  • anonymous
you are awesomely amazing and i love you for it. lol. sorry im really happy.
mathstudent55
  • mathstudent55
No problem, and you are very welcome. Just one quick check. Since we know this is a 30-60-90 triangle with a 90 degree angle and a 30 degree angle, the third angle had better be 60 degrees. Sure enough, \( \dfrac{\pi}{3}rad = \dfrac{180^{\circ}}{3} = 60 ^ {\circ} \)
mathstudent55
  • mathstudent55
I like the way you went from "lost and confused and pissed off" to "im really happy" Keep studying and asking questions. This is how you learn.

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