Sample Problems on How to determine the length of a Shadow?

Problem 1. Find the length of the shadow of an object at a height of 5 m if the angle of elevation is 45^o.

Solution:

We have,

h = 5

θ = 45^o

Using the formula for shadow length, we have

s = h/tan θ

= 5/tan 45^o

= 5/1

= 5 m

Problem 2. Find the length of the shadow of an object at a height of 7 m if the angle of elevation is 60^o.

Solution:

We have,

h = 7

θ = 60^o

Using the formula for shadow length, we have

s = h/tan θ

= 7/tan 60^o

= 7/√3

= 4.04 m

Problem 3. Find the length of the shadow of an object at a height of 12 m if the angle of elevation is 30^o.

Solution:

We have,

h = 12

θ = 30^o

Using the formula for shadow length, we have

s = h/tan θ

= 12/tan 30^o

= 12/(1/√3)

= 20.78 m

Problem 4. Find the height of an object if the shadow length is 9 m and the angle of elevation is 55^o.

Solution:

We have,

s = 9

θ = 55^o

Using the formula for shadow length, we have

s = h/tan θ

=> 9 = h/tan 55^o

=> h = 9 tan 55^o

=> h = 9 (1.43)

=> h = 12.87 m

Problem 5. Find the height of an object if the shadow length is 14 m and the angle of elevation is 65^o.

Solution:

We have,

s = 14

θ = 65^o

Using the formula for shadow length, we have

s = h/tan θ

=> 14 = h/tan 65o

=> h = 14 tan 65o

=> h = 14 (2.144)

=> h = 30.01 m

Problem 6. Find the angle of elevation if the object has a height of 4 m and the shadow length is 9.42 m.

Solution:

We have,

h = 4

s = 9.42

Using the formula for shadow length, we have

s = h/tan θ

=> tan θ = h/s

=> tan θ = 4/9.42

=> tan θ = 0.42

=> θ = 23^o

Problem 7. Find the angle of elevation if the object has a height of 16 m and a shadow length is 21.22 m.

Solution:

We have,

h = 16

s = 21.22

Using the formula for shadow length, we have

s = h/tan θ

=> tan θ = h/s

=> tan θ = 16/21.22

=> tan θ = 0.75

=> θ = 37^o

To find the length of a shadow, you need to know the angle of the light source and the distance from the object to where the shadowlands. Measure how far the object is from the spot where its shadow touches the ground. Then, multiply this distance by the tangent of the light source’s angle. If the angle is less than 10 degrees, you can use this simple formula: Length of Shadow = Distance to Shadow Point × tan(Angle of Light). For greater accuracy or larger angles, you might need more complex math.