Question

a gate that is 5 ft tall casts a shadow 9 ft long the house behind the gate cast a shadow of 54 ft how about how many feet tall is the house

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

gate:

hg = 5 ft

shadow = 9ft

house

hh = ?

shadow = 54 ft

Step 02:

We must apply the theorem of thales.

$\frac{hg}{hh}=\frac{shadow\text{ gate}}{\text{shadow house}}$$\frac{5ft}{hh}=\frac{9ft}{54\text{ ft}}$

hh * 9 ft = 5 ft * 54 ft

hh = (5 ft * 54 ft ) / 9 ft

hh = 270 ft ² / 9 ft = 30 ft

The answer is:

The house is 30ft tall.