Question

On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?

Answer 1

the length of the shadow is 30m

Step-by-step explanation:

hypotenuse = 50m

height of tree = 40 m

To solve the question, we will use an illustration:

To get the length of the shadow, we will apply pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

hypotenuse = 50m, opposite = 40m

50² = 40² + shadow²

2500 = 1600 + shadow²

2500 - 1600 = shadow²

900 = shadow²

square root both sides:

`\begin{gathered} \sqrt[]{900}\text{ = }\sqrt[]{shadow^2} \\ \text{shadow = 30 m} \end{gathered}`

Hence, the length of the shadow is 30m