The length of AB = 23.
Solution:
Given ABC is a triangle.
BC = a = 49 m
AC = b = 56 m
∠C = 24°
Let AB = c
To find the length of AB:
Use cosine law,
[tex]c^{2}=a^{2}+b^{2}-2 a b \cos C[/tex]
[tex]c^{2}=49^{2}+56^{2}-2 (49)(56) \cos 24^\circ[/tex]
[tex]c^{2}=2401+3136-5488 \cos 24^\circ[/tex]
[tex]c^{2}=5537-5488 \cos 24^\circ[/tex]
The value of cos 24° = 0.9135
[tex]c^{2}=5537-5488(0.9135)[/tex]
[tex]c^{2}=5537-5013.288[/tex]
[tex]c^{2}=523.712[/tex]
Take square root on both sides of the equation.
c = 22.88
c = 23 (rounding off to nearest value)
The length of AB = 23.
