Answer:
The distance between deer A and C is 122 m
Explanation:
Hi there!
For this problem, we can use the law of sines. Please, see the attached figure for a better understanding of the problem.
From the law of sines:
sin β / side BC = sin θ/ side AB = sin α / side AC
The angle β can be calculated (see figure):
β = 180° - 52.4° - 77.3° = 50.3°
Then, we can find the angle θ :
sin β / side BC = sin θ/ side AB
sin 50.3° / 94.8 m = sin θ / 63.4 m
63.4 m · (sin 50.3° / 94.8 m) = sin θ
θ = 31.0°
Now, we can calculate the angle α. The sum of the internal angles of a triangle is 180°. Then:
α = 180° -31.0° - 50.3° = 98.7°
Using the laws of sines:
sin α / side AC = sin θ / side AB
sin 98.7°/ side AC = sin 31.0°/ 63.4 m
side AC = sin 98.7 / ( sin 31.0°/ 63.4 m)
side AC = 122 m
The distance between deer A and C is 122 m
