Question

Solve the triangle, given the following : angle A= 30, side b= 6 , and side c=8
find angle C, Angle B, and side a?

Answer 1

well the triangle looks like



find a by using the law of cosines

then find B using the law of Sines

then find C using angle sum of a triangle

hope it helps

Answer 2

a=9.2 , i tried to use law of sine , but the answer didn't make sense

Answer 3

sinB/6 = sine30/9.23 ..... couldn't get a realistic solution from it

Answer 4

the law of sines says

\[\frac{\sin(30)}{9.2} = \frac{\sin(B)}{6}\]

Answer 5

so

\[\sin(B) = \frac{6 \times \sin(30)}{9.2}\]

you will get a decimal less than 1...

then its \[B = \sin^{-1}(answer) \]

Answer 6

and you may like to check your solution to a

Answer 7

I got a negative solution, won't that be undefined .. because the limit is 0-1?

Answer 8

ok.... go back to the law of cosines

\[a^2 = 6^2 + 8^2 - 2 \times 6 \times 8 \times \cos(30)\]

Answer 9

by my calculations its not 9.2

Answer 10

if you look at the triangle the angle of 30 is opposite the longest side 9.2 so B and C would need to be less than 30... so its not a triangle

Answer 11

still there @moonlight93

Answer 12

so would that be "can not be solved" ?

Answer 13

no... go back and redo the law of cosines... as your answer is incorrect for a

I posted it correctly above...

Answer 14

I still don't get it. i've been trying over and over. do you know the answer of angle B ?

Answer 15

ok...

\[a^2 = 6^2 + 8^2 - 2 \times 6 \times 8 \times \cos(30)\]

\[a^2 = 100 - 83.14\]

what is the value of a...?

Answer 16

a=4.106

Answer 17

but why did you get a 83.14 for the right side?

I got 100-14.808 ... and that's how I got the 9.23

Answer 18

great... so now the measurements make sense

then

\[\frac{\sin(30)}{4.1} = \frac{\sin(B)}{6}\]

so

sin(B) = 0.731717

Answer 19

so then

\[B = \sin^{-1}(0.731707)\]

then find C using angle sum of a triangle.

Answer 20

83.2....= 2 x 6 x 8 cos(30)

Answer 21

I have to go... Hope its helped.

Answer 22

ok, thank you

Answer 23

@@ is your triangle even a right triangle?

Answer 24

@campbell_st ... sorry yes it will equal 83.2 .. my calculator was in radians mode, I got that answer when i swiched to degree mode. thank you for helping :)

Answer 25

@BabiiMuffin , it doesn't say it is. we've been studying both non-right and right triangle.. though we suppose to solve as if it's a non-triangle.