Answer:
1. Length BC is 1200 ft
2. Angle B is 48.6°
3. Angle C is 41.8°
Step-by-step explanation:
1. Determination of the length BC
Side opposite C = c = 800 ft
Side opposite B = b = 900 ft
Angle A = 89.6°
Side opposite BC = a =?
Using cosine rule, we can obtain length BC as follow:
a² = b² + c² – 2bc CosA
a² = 900² + 800² – 2 × 900 × 800 × Cos89.6
a² = 810000 + 640000 – 1440000 × 0.007
a² = 1450000 – 10080
a² = 1439920
Take the square root of both side
a = √1439920
a ≈ 1200 ft
Thus, length BC is 1200 ft
2. Determination of angle B
Side opposite B = b = 900 ft
Side opposite A = a = 1200 ft
Angle A = 89.6°
Angle B =?
Angle B can be obtained by using sine rule as follow:
a / Sine A = b / Sine B
1200 / Sine 89.6° = 900 / Sine B
Cross multiply
1200 × Sine B = 900 × Sine 89.6°
1200 × Sine B = 900
Divide both side by 1200
Sine B = 900/1200
Sine B = 0.75
Take the inverse of Sine
B = Sine¯¹ 0.75
B = 48.6°
Thus, angle B is 48.6°
3. Determination of angle C
Side opposite C = c = 800 ft
Side opposite A = a = 1200 ft
Angle A = 89.6°
Angle C =?
Angle C can be obtained by using sine rule as follow:
a / Sine A = c / Sine C
1200 / Sine 89.6° = 800 / Sine B
Cross multiply
1200 × Sine C = 800 × Sine 89.6°
1200 × Sine C = 800
Divide both side by 1200
Sine C = 800/1200
Sine C = 0.6667
Take the inverse of Sine
C = Sine¯¹ 0.6667
C = 48.6°
Thus, angle C is 41.8°
