Question

Suppose angle a=pi/6 radians and length of b=5

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

oops that's the cosine

Answer 11

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

Answer 12

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

Answer 13

yea, now try again

Answer 14

math, she is faster than you think ;)

Answer 15

:) cosine 30=5/c

Answer 16

we know that cosine is sqrt3/2

Answer 17

good! so c = ... ?

Answer 18

c=10/sqrt(3)?

Answer 19

yessss!

now onto a

Answer 20

we can use tan30=a/5

Answer 21

so a =... ?

Answer 22

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

Answer 23

sqrt 3/ 3 = 1/sqrt 3

Answer 24

5sqrt(3)/3?

Answer 25

yes, correct!

5 (sqrt 3)/3 or 5/ sqrt 3

Answer 26

one good way to verify,

side opposite to 30 degree angle should come out to be half the hypotenuse :)

Answer 27

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:

\(\tan A = \dfrac{opp}{adj} \)

\(\tan \dfrac{\pi}{6} = \dfrac{a}{5}\)

\(a = 5 \tan \frac{\pi}{6} \)

\(a = \dfrac{5 \sqrt{3}}{3} \)

Answer 28

\(\sin A = \dfrac{opp}{hyp}\)

\(\sin \dfrac{\pi}{6} = \dfrac{\frac{5\sqrt{3}}{3}}{c}\)

\(\dfrac{1}{2} = \dfrac{\frac{5\sqrt{3}}{3}}{c}\)

\(c = \dfrac{10\sqrt{3}}{3}\)