Question

How many feet ??? Please help

Answer 1

Answer:

11 feet

Step-by-step explanation:

This is a right triangle trig problem with a little geometric twist to it.  The angle of depression.  If we drew this triangle and the person at the top of it and then drew in a horizontal line from his line of vision, this line of vision is parallel with the ground.  The hypotenuse (escalator, here) serves as the transversal cutting these parallel lines.  That means that a lot of angle congruencies exist.  The angle of depression is alternate interior with the base angle of the triangle (the angle that is NOT the right angle, that is) so that makes them congruent.  Therefore, we have that base angle measuring 42.51 degrees (this is the reference angle) and the length of the hypotenuse.  We are looking for the height of the triangle, which is also the side across from the reference angle.  The trig ratio we need to solve this has to involve the reference angle, the hypotenuse, and the side across from the reference angle.  That is the sin ratio.  Setting up to solve for the side across from the angle:

$sin(42.51)=\frac{y}{16}$

Solving for y:

16 sin(42.51) = y

Do this on your calculator in degree mode to get that

y = 10.8 feet, or rounding, y = 11