Answer Question in image attached :)
20 points !

Plane A because it was 7.62 miles away.

Seems like options are wrong. Because plane A will be 27.43 miles away if it was 18 miles from the ground. And Plane A 20.71 miles away with different angle.

Step-by-step explanation:

This question is based on the topic Trigonometry where we'll make use formula: sinØ = Perpendicular/Hypotenuse. Let's understand the given question first. Here we are provided with two aeroplanes which leaves the airport. Plane A departs at 41° angle from the runway and plane B departs at a 43° angle from the runway. Now of all, we have to find that which plane was further away from the airport when it was 5 miles from the ground. Let's make use of Trigonometry.

Plane A departs at 41° angle from the runway and plane B departs at a 43° angle from the runway when it was 5 miles away from the ground.

For plane A: Angle is 41° and perpendicular distance (that is distance covered from the start to flight) is 5 miles. And what asked in question is 'which plane is farther away' means at what distance is plane A and B is and out of plane A and B which one is farther away.

⇒ sinØ = Perpendicular/Hypotenuse

⇒ sin41° = 5/Hypotenuse

⇒ 0.6561 = 5/Hypotenuse

⇒ Hypotenuse = 5/0.6561

⇒ Hypotenuse = 7.62 miles (Plane A)

Similarly for plane B,

⇒ sin43° = 5/Hypotenuse

⇒ Hypotenuse = 5/0.682

⇒ Hypotenuse = 7.33 miles (Plane B)

In a nutshell hypotenuse of plane A >>>> hypotenuse of plane B. Hence, plane A was farther away from the airport when it was 5 miles from the ground.