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

1. anonymous

2. 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.

3. anonymous

so angle A=30 degrees, and angle b=60 degrees

4. mathstudent55

What is the sum of the measures of the angles of a triangle?

5. anonymous

the sum is 180 degrees.. got that down :) I'm just having trouble with finding the lengths.

6. mathstudent55

Angle A does not measure 30 deg. Also, they want the answer in radians.

7. hartnn

she has done similar problems before :) what have you tried for a and c ?

8. anonymous

if you convert 30 degrees into radians you get pi/6

9. anonymous

sin30=5/c, c*sin30=5,c=5/sin30, 5 divided by 1/2, = 5*2 which is 10

10. hartnn

sin 30 = 5/c sure?? B is 60 degrees

11. anonymous

oops that's the cosine

12. 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<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

13. mathstudent55

Now let's look at finding the length of a.

14. hartnn

yea, now try again

15. hartnn

math, she is faster than you think ;)

16. anonymous

:) cosine 30=5/c

17. anonymous

we know that cosine is sqrt3/2

18. mathstudent55

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19. hartnn

good! so c = ... ?

20. anonymous

c=10/sqrt(3)?

21. mathstudent55

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22. hartnn

yessss! now onto a

23. anonymous

we can use tan30=a/5

24. hartnn

so a =... ?

25. anonymous

well we know that tan 30=sqrt(3)/3

26. hartnn

sqrt 3/ 3 = 1/sqrt 3

27. anonymous

5sqrt(3)/3?

28. hartnn

yes, correct! 5 (sqrt 3)/3 or 5/ sqrt 3

29. hartnn

one good way to verify, side opposite to 30 degree angle should come out to be half the hypotenuse :)

30. 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: $$\tan A = \dfrac{opp}{adj}$$ $$\tan \dfrac{\pi}{6} = \dfrac{a}{5}$$ $$a = 5 \tan \frac{\pi}{6}$$ $$a = \dfrac{5 \sqrt{3}}{3}$$

31. mathstudent55

$$\sin A = \dfrac{opp}{hyp}$$ $$\sin \dfrac{\pi}{6} = \dfrac{\frac{5\sqrt{3}}{3}}{c}$$ $$\dfrac{1}{2} = \dfrac{\frac{5\sqrt{3}}{3}}{c}$$ $$c = \dfrac{10\sqrt{3}}{3}$$