Answer:
angle BAC = 57.84°
Step-by-step explanation:
To find angle BAC given AB=6cm BC= 13 cm and ACB=23°
we will follow the steps below;
we can use the sine formula to solve the problem given
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin C}{c}[/tex]
from the question given;
A = ?
C = 23°
c=AB = 6 cm
a=BC = 13 cm
substitute the values into the formula above
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin C}{c}[/tex]
[tex]\frac{sin A}{13}[/tex] = [tex]\frac{sin 23}{6}[/tex]
cross -multiply
6 sinA = 13 sin23°
sin A = 13 sin23° / 6
sin A = 0.84658
take the [tex]sin^{-1}[/tex] of both-side
[tex]sin^{-1}[/tex] sin A = [tex]sin^{-1}[/tex] (0.84658)
on the left-hand side of the equation [tex]sin^{-1}[/tex] will cancel-out sin leaving us with just A
A = [tex]sin^{-1}[/tex] (0.84658)
A ≈ 57.84°
angle BAC = 57.84°
