I NEED DETAILED explanation because I should be getting this right!

Question

Three people are watching a hot air balloon travel over their town. At a certain point in time, one person stands directly below the balloon, and the others look at it at certain angles. In the following image, A, B, and C are people, and D is the balloon. Person C is 384m directly below the balloon, Person B is 200m away from Person C, and the angle between Person A, the balloon, and Person B is 33o. How far is Person A from the hot air balloon?

Answer 1

About 386

or 385.77 m

AD = 384/cos5.88 = 385.77

5.88 = 33-27.512

90-62.488 = 27.512

tan62.488 = 384/200 = 1.92

angle whose tangent = 1.92 = 62.488

draw a triangle from A to D to B

slice it in two with two triangles, right triangles

ADC and BDC

calculate sides of the triangles with sines and cosines.