(9CQ) Find the distance from the balloon to the soccer fields.

Answer:The distance from the balloon to the soccer fields = 3.6 miles ⇒ answer (b)Step-by-step explanation:* Let the hot air balloon  at point A , the soccer fields   at point B and the football field at point C∵ The measure of the angle of depression to the    soccer fields is 20° 15'∴ The measure of angle B = 20° 15'∵ The measure of the angle of depression to the    football field is 62° 30'∴ The measure of angle C = 62° 30'∵ The sum of measures of the interior angles of any triangle = 180°∴ The measure of angle A = 180 - (20° 15' + 62° 30') = 97° 15'* The distance between the balloon and the soccer field   is represented by the side AB of triangle ABC- Use the sin Rule to find the length of side AB∵ a/sin(A) = b/sin(B) = c/sin(C)- a is the side opposite to angle A, b is the side opposite  to angle B and c is the side opposite to angle C∵ AB = c ⇒ opposite to angle C∵ The distance between the two fields = 4 miles∴ BC = 4 miles ∵ BC = a ⇒ opposite to angle A∴ 4/sin(97° 15') = c/sin(62° 30')∴ c = (4 × sin(62° 30')) ÷ sin(97° 15')∴ c = 3.6 miles∴ The distance from the balloon to the soccer fields = 3.6 miles    answer (b)