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.

Explanation:

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

`(x_1)/(y_1)=(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

`(x)/(34)=(78)/(56)\\\\\Rightarrow\ x=(78*34)/(56)\\\\\Rightarrow\ x=47.3571428571\approx47.36`

Hence, the height of tree = 47.36 feet.