Question

Jonathan is standing atop a building and looking at a parking lot in the distance. He is 6 feet tall, the angle of depression is 30°, and the height of the building is 80 feet. Drag the values to the correct locations in the diagram representing this situation.

Answer 1

Lets draw a diagram of the situation.

We have the triangle ABC, so lets solve it:
We know that the depression angle is 30°; the angle of depression is the angle between the horizontal an the line of sight of the observer. We can infer form our diagram that the angle between the horizontal line and the vertical line formed by the person and the building is 90°, so the mesaure of angle A will be 90 ° minus the measure of the depression angle:
$A=90-30$
$A=60$°

Now, to find angle C, we are going to take advantage of the fact that the sum of the interior angles of a triangle is always 180°:
$C=180-(60+90)$
$C=30$°

To find the distance $b$ between Jonathan and the parking lot, we are going to use sine trigonometric function:
$sin(C)= \frac{opposite.side}{hypotenuse}$
$sin(30)= \frac{86}{b}$
$b= \frac{86}{sin(30)}$
$b=172$ feet 

To find the distance $a$ from the parking lot to the base of the building, we are going to use the Pythagorean theorem:
$a^2=hypotenuse^2-leg^2$
$a^2=172^2-86^2$
$a= \sqrt{172^2-86^2}$
$a=148.96$ feet 

We can conclude that the values to the correct locations in the diagram representing this situation are: