- #1

chwala

Gold Member

- 2,697

- 360

- Homework Statement
- See attached.

- Relevant Equations
- Trigonometry

Question;

My take,

I have,

then

using sine rule;

##\dfrac{x}{x+y} = \dfrac{\sin 20^{\circ}}{\sin 80^{\circ}}##

##\dfrac{x}{x+y} =0.347##

##x=3.47## then ##y=6.53##.

then,

##BD^2=3.47^2+10^2-(2×3.47×10×\cos 20^{\circ})##

##BD= 6.842##

...

##10^2=3.47^2+6.842^2-(2×3.47×6.842 ×\cos m)##

##41.15=-47.4696\cos m##

##\cos m = -0.866##

##m= 150^{\circ}##

there could be a better approach...just came across this question today.

My take,

I have,

then

using sine rule;

##\dfrac{x}{x+y} = \dfrac{\sin 20^{\circ}}{\sin 80^{\circ}}##

##\dfrac{x}{x+y} =0.347##

##x=3.47## then ##y=6.53##.

then,

##BD^2=3.47^2+10^2-(2×3.47×10×\cos 20^{\circ})##

##BD= 6.842##

...

##10^2=3.47^2+6.842^2-(2×3.47×6.842 ×\cos m)##

##41.15=-47.4696\cos m##

##\cos m = -0.866##

##m= 150^{\circ}##

there could be a better approach...just came across this question today.