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)
