Question

There is an escalator that is 1086.8 feet long and drops a vertical distance of 195.4 feet. What is its angle of​ depression?

Answer 1

`" "`
Angle of Depression `color(blue)([ theta ] ~~ 10.36^@`

Explanation:

`" "`

`color(green)("Step 1:"`

Draw a rough sketch with input data given in the problem:

Angle of depression is measured from the Line of Vision.

`color(green)("Step 2:"`

Find the angle of depression `alpha, /_DBC`.

Observe that `/_DBC = /_ACB` are alternate angles and they are congruent.

`:. /_DBC = /_ACB = alpha`

`color(green)("Step 3:"`

Consider the angle `theta, /_ ACB`

To find `theta`, use the `sin` ratio: `sin(theta)=("Opposite Side")/("Hypotenuse")=(AB)/(BC)`

`rArr sin(theta)=195.4/1086.8`

`rArr sin(theta) ~~ 0.17979384`

`color(green)("Step 4:"`

To find `color(blue)(theta`, find `color(red)(sin^-1(theta)`

`color(red)(theta=sin^(-1)(0.17979384)`

Hence, `color(green)((theta)~~ 10.35775471^@`

Angle of Depression: `color(blue)( theta ~~ 10.36^@`

Hope it helps.