Question

May I please receive help?

Answer 1

Answer:

Length of the shadow = 20.5 cm

Step-by-step explanation:

Given the 32-meter height of a tall building, and its casted shadow of 38 meters, we can find the unknown length of the shadow by using the Pythagorean Theorem.

Definition:

The Pythagorean Theorem states that the squared length of the hypotenuse of a right triangle is equal to the sum of the squared lengths of the legs.

The algebraic representation of the Pythagorean Theorem is:  

                     c² (hypotenuse) = a² (leg₁) + b² (leg₂)

Solution

To solve for the given problem:

Let c = 38 m (distance from the top of the building to the tip of the shadow)

a = unknown length of the shadow

b = 32m (height of the building)

Since we have to solve for the value of a (unknown length of the shadow), we must algebraically solve for a:

c² = a² + b²

Subtract b² from both sides:

c² - b² = a²  + b² - b²

a² = c² - b²

Substitute the given values into the formula for solving a :

a² = c² - b²

a² = (38)² - (32)²

a² = 1444 - 1024

a² = 1444 - 1024

Next, take the square root of both sides to solve for a:

$\displaystyle\mathsf{\sqrt{(a)^2}\:=\:\sqrt{420}}$

a = 20.49 or 20.5 cm

Therefore, the length of the shadow is 20.5 cm.