Question

A person 1.65m tall casts 1.8m shadow. At the same instance, a lamp-posts casts a shadow of 5.4 m. Find the height of the lamppost.

Answer 1

We can begin by creating a ratio of the length of the shadow to the height of the person. This would become $\frac{1.8}{1.65}$

We can then set that equal to the ratio of the lamppost $\frac{1.8}{1.65} =\frac{5.4}{x}$

We then can cross multiply, which will give us (5.4)(1.65) = 1.8x

This simplifies to 8.91 = 1.8x

Then we can divide each side by 1.8

this gives us x = 4.95 m, which is the height of the lamppost

Answer 2

1.65 m =  1.8 m shadow

Find the height of the object of 1 m shadow:

1.8 m shadow = 1.65 m

1 m shadow = 1.65 ÷ 1.8 = 11/12 m

Find the height of the object of 5.4 m shadow:

5.4 mm shadow = 11/12 x 5.4 = 4.95 m

Answer: The lamp post is 4.95 m