Shadow Length Calculator

The angle of elevation is also required to compute an object's shadow. Depending on the time of day, the shadow length increases and decreases. The shadow is cast on the opposite side, and its length is calculated using the formula below.

Shadow Length L = h/ tan α

• L be the Length of the shadow
• h is the height of the object
• α denoted as the angle of elevation of the sun

If there is no shadow, the calculator returns zero. As you may be aware, this can occur at any time of day or night. When the sun is at an angle 45°, the object's length is equal to the length of its shadow.

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The length of your shadow is determined by your height and the position of the sun or other source of light behind you in respect to the ground. The length of the shadow is proportional to the angle of the sun. In addition, the longer the shadow, the taller you are.

• Determine the height first: The height of the person or object should be measured or calculated.
• Next, determine the light's angle to calculate the angle between the shadow's surface and the source of light.
• Finally, figure out how long the shadow will be using the equation above, determine the length of the shadow.

Question 1: Consider a 15m long pole casting a shadow. If the angle of elevation of the sun is 45°, What will be the length of the shadow?

Solution:

Consider the problem, we have

The angle of elevation of the sun α is 45°

The long pole casting a shadow h = 15m

We know the formula to calculate Shadow Length L = h/ tan α

• L be the Length of the shadow
• h is the height of the object
• α denoted as the angle of elevation of the sun

Substituting the inputs, we get the following equation for shadow length

L = 15/ tan 45°

L = 15/1 (Since, tan 45°=1)

L = 15 m

Therefore, The Shadow Length = 15 m

Note:When the sun is at an angle 45°, the object's length is equal to the length of its shadow.

1. How to calculate the shadow length using calculator?

To determine the shadow length, enter the object's height and the angle of the light source measured from the ground.

2. What exactly is a shadow?

The blocking of a light source from the reflecting surface causes a shadow, which is a darker reflection of an object.

3. How can you figure out how long a shadow is?

Replace the numerical equivalents in the following formula: Shadow Length = Object Height / tan α.

4. What is the meaning of the shadow rule?

By observing the length of a person's shadow over the course of a day, the shadow rule indirectly estimates the sun's altitude.