Question

ABC represents a race path. Find the total distance of the race. Round your answer to the nearest meter.

Answer 1

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,

$\frac{SinB}{AC}=\frac{SinA}{BC}=\frac{SinC}{AB}$

$\frac{Sin35}{450}=\frac{Sin85}{AC}=\frac{Sin60}{AB}$      [Since m∠A = 180° - (85 + 60)° = 35°]

$\frac{Sin35}{450}=\frac{Sin85}{AC}$

AC = $\frac{450\times \text{Sin85}}{\text{Sin35}}$

     = 781.57 meters

$\frac{Sin35}{450}=\frac{Sin60}{AB}$

AB = $\frac{450\times \text{Sin60}}{\text{Sin35}}$

     = 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.