Question

Trigonometry: How to Compute the length of my shadow using a clinometer?

Answer 1

Using the clinometer, measure the angle of depression of the tip of your shadow and call it θ. You will need h, the height of the clinometer.

Draw a triangle. Let x=length of shadow. θ is also the angle of elevation pointing to the clinometer.

tan(θ)=h/x

Answer 2

You measure 30° and you know your eye height is 143 cm,

tan(30)=143/x

x=143/tan(30)=248 cm=

shadow length

You are done

Answer 3

Wait now i think, so when i get the x I’ll just have to add the value difference between the eye height and the whole height so i will get the total value of my shadow length?

1st Example:

I get 30 degrees from the Clinometer as an angle of depression

30-90= 60 degrees

Now the elevation and depression is 60 degrees.

X (Adjacent)

my eye height is 143 cm (Opposite)

Then the angle is 60 degrees (Theta)

We will use Tangent

x=143/tan(60) = 82.56

Now my whole height is 153

The difference value of my eye height and whole height is 10 because 143-153 = 10

85.56+10=95.56

Length of my shadow is 95.56cm

2nd Example: Instead of using my eye height, i will get the length of shadow using my whole height.

153/Tan(60)=88.33

Therefore my shadow length is 88.33 cm

Which one is the right one? The 1st example or 2nd example?

I am in hurry so i can’t provide the full solution sorry