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anonymous
 one year ago
Suppose angle a=pi/6 radians and length of b=5
anonymous
 one year ago
Suppose angle a=pi/6 radians and length of b=5

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2There 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
 one year ago
Best ResponseYou've already chosen the best response.0so angle A=30 degrees, and angle b=60 degrees

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2What is the sum of the measures of the angles of a triangle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the sum is 180 degrees.. got that down :) I'm just having trouble with finding the lengths.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Angle A does not measure 30 deg. Also, they want the answer in radians.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1she has done similar problems before :) what have you tried for a and c ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you convert 30 degrees into radians you get pi/6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sin30=5/c, c*sin30=5,c=5/sin30, 5 divided by 1/2, = 5*2 which is 10

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1sin 30 = 5/c sure?? B is 60 degrees

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops that's the cosine

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Yes, 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<A + m<B + 90 = 180 m<A + m<B + pi/2 = pi pi/6 + m<B + pi/2 = pi pi/6 + m<B + 3pi/6 = 6pi/6 m<B = 2pi/6 m<B = pi/3

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now let's look at finding the length of a.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1math, she is faster than you think ;)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we know that cosine is sqrt3/2

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443985244529:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443985322492:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we can use tan30=a/5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well we know that tan 30=sqrt(3)/3

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yes, correct! 5 (sqrt 3)/3 or 5/ sqrt 3

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1one good way to verify, side opposite to 30 degree angle should come out to be half the hypotenuse :)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2We 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
 one year ago
Best ResponseYou've already chosen the best response.2\(\sin A = \dfrac{opp}{hyp}\) \(\sin \dfrac{\pi}{6} = \dfrac{\frac{5\sqrt{3}}{3}}{c}\) \(\dfrac{1}{2} = \dfrac{\frac{5\sqrt{3}}{3}}{c}\) \(c = \dfrac{10\sqrt{3}}{3}\)
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