Answer:
Race covers 1911 meters.
Step-by-step explanation:
Triangle ABC represents a race path.
Total distance covered by the race = Perimeter of the triangle ABC
We will apply Sine rule in the given triangle to find the unknown sides.
By Sine rule,
[tex]\frac{SinB}{AC}=\frac{SinA}{BC}=\frac{SinC}{AB}[/tex]
[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}=\frac{Sin60}{AB}[/tex] [Since m∠A = 180° - (85 + 60)° = 35°]
[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}[/tex]
AC = [tex]\frac{450\times \text{Sin85}}{\text{Sin35}}[/tex]
= 781.57 meters
[tex]\frac{Sin35}{450}=\frac{Sin60}{AB}[/tex]
AB = [tex]\frac{450\times \text{Sin60}}{\text{Sin35}}[/tex]
= 679.44 meters
Perimeter of the triangle = AB + BC + AC
= 679.44 + 450 + 781.57
= 1911.01
≈ 1911 meters
Therefore, the race covers 1911 meters.
