Question

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

Answer 1

1911

Explanation:

yes

Answer 2

Race covers 1911 meters.

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,

`(SinB)/(AC)=(SinA)/(BC)=(SinC)/(AB)`

`(Sin35)/(450)=(Sin85)/(AC)=(Sin60)/(AB)` [Since m∠A = 180° - (85 + 60)° = 35°]

`(Sin35)/(450)=(Sin85)/(AC)`

AC =
`\frac{450* \text{Sin85}}{\text{Sin35}}`

= 781.57 meters

`(Sin35)/(450)=(Sin60)/(AB)`

AB =
`\frac{450* \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.