Question

The shadow cast by an object on a sunny day is directly proportional to the height of the object. If a person 78 inches tall casts a shadow 56 inches​ long, how tall is a tree which casts a shadow 34 feet in​ length? Round to the nearest hundredth if necessary.

Answer 1

Answer: 47.36 feet.

Step-by-step explanation:

When two quantities x and y are directly proportional , then the equation that shows direct variation is given by :-

$\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}$

Given : The shadow cast by an object on a sunny day is directly proportional to the height of the object.

Let x be the height of tree.

According to the the given question , we have

$\dfrac{x}{34}=\dfrac{78}{56}\\\\\Rightarrow\ x=\dfrac{78\times34}{56}\\\\\Rightarrow\ x=47.3571428571\approx47.36$

Hence, the height of tree = 47.36 feet.