anonymous
  • anonymous
Suppose angle a=pi/6 radians and length of b=5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
mathstudent55
  • mathstudent55
There are 3 angles in your triangle. One measures pi/3. Another angle is a right angle. You can calculate the measure of the third angle.
anonymous
  • anonymous
so angle A=30 degrees, and angle b=60 degrees

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More answers

mathstudent55
  • mathstudent55
What is the sum of the measures of the angles of a triangle?
anonymous
  • anonymous
the sum is 180 degrees.. got that down :) I'm just having trouble with finding the lengths.
mathstudent55
  • mathstudent55
Angle A does not measure 30 deg. Also, they want the answer in radians.
hartnn
  • hartnn
she has done similar problems before :) what have you tried for a and c ?
anonymous
  • anonymous
if you convert 30 degrees into radians you get pi/6
anonymous
  • anonymous
sin30=5/c, c*sin30=5,c=5/sin30, 5 divided by 1/2, = 5*2 which is 10
hartnn
  • hartnn
sin 30 = 5/c sure?? B is 60 degrees
anonymous
  • anonymous
oops that's the cosine
mathstudent55
  • mathstudent55
Yes, you are correct. I was thinking of angle B, which is the one they are asking for. 180 deg = pi rad The sum of the measures of the angles of a triangle is 180 deg = pi rad. m
mathstudent55
  • mathstudent55
Now let's look at finding the length of a.
hartnn
  • hartnn
yea, now try again
hartnn
  • hartnn
math, she is faster than you think ;)
anonymous
  • anonymous
:) cosine 30=5/c
anonymous
  • anonymous
we know that cosine is sqrt3/2
mathstudent55
  • mathstudent55
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hartnn
  • hartnn
good! so c = ... ?
anonymous
  • anonymous
c=10/sqrt(3)?
mathstudent55
  • mathstudent55
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hartnn
  • hartnn
yessss! now onto a
anonymous
  • anonymous
we can use tan30=a/5
hartnn
  • hartnn
so a =... ?
anonymous
  • anonymous
well we know that tan 30=sqrt(3)/3
hartnn
  • hartnn
sqrt 3/ 3 = 1/sqrt 3
anonymous
  • anonymous
5sqrt(3)/3?
hartnn
  • hartnn
yes, correct! 5 (sqrt 3)/3 or 5/ sqrt 3
hartnn
  • hartnn
one good way to verify, side opposite to 30 degree angle should come out to be half the hypotenuse :)
mathstudent55
  • mathstudent55
We know the measure of angle A and the length of the adjacent side, b. We want the length of the opposite side, a. The tangent function relates the lengths of the opposite and adjacent sides: \(\tan A = \dfrac{opp}{adj} \) \(\tan \dfrac{\pi}{6} = \dfrac{a}{5}\) \(a = 5 \tan \frac{\pi}{6} \) \(a = \dfrac{5 \sqrt{3}}{3} \)
mathstudent55
  • mathstudent55
\(\sin A = \dfrac{opp}{hyp}\) \(\sin \dfrac{\pi}{6} = \dfrac{\frac{5\sqrt{3}}{3}}{c}\) \(\dfrac{1}{2} = \dfrac{\frac{5\sqrt{3}}{3}}{c}\) \(c = \dfrac{10\sqrt{3}}{3}\)

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