Question

"the balcony seats at the opera house have an angle of depression of 55° to center stage. if the horizontal (ground) distance to the center of the stage is 50 feet, how far are the patrons in the balcony to the singer at center stage? " (young 59) young, cynthia y. trigonometry, 3rd edition. wiley, 09/2011. vitalbook file.

Answer 1

In dealing with these problems, the first step to do is illustrate it. When you do, you would see a right triangle with a 55° angle between the hypotenuse and the vertical leg. Using pythagorean relations:

sin 55 = 50/x, where x is the unknown
x =50/sin55
x = 61.04 feet