Question

You sit in the bleachers at a concert. The angle of depression from your horizontal sight to the stage is 24 degrees. If your seat is 45 feet above the stage level what is your actual distance d from the stage

Answer 1

Answer:

x=111ft

Step-by-step

sin 24 = 45/x

+ the parallel lines

45 +x+24

x= 45/sin 24

Answer 2

The actual distance of your from the stage is 111 feet.

What is angle of depression?

The angle formed by the line of sight and the horizontal plane for an object below the horizontal is called angle of depression.

What is sine of an angle?

The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.

According to the given question

We have

Angle of depression = 24degrees.

Let d be the actual distance of your from the stage.

Now in right angle triangle ABC

We have

AC = 45 feet

And, ∠ABC = 24 degrees

Now the Sine of an angle ∠ABC is given by

$sin24 = \frac{AC}{AB}$

⇒$sin24=\frac{45}{d}$

⇒ $0.406=\frac{45}{d}$

⇒ $d =\frac{45}{0.406}$

⇒$d = 110.64 feet$ or $111feet$

Hence, the actual distance of your from the stage is 111 feet.

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