Question

keenan sees a maple tree and an observation tower. the maple tree is 12 meters tall and casts a shadow that is 9 meters long. what is the height of the observation tower if the observation towers shadow is 12 meters long? write your answer as a whole number or a decimal. do not round. meters

Explanation:

Step1: Set up the proportion

Since the ratio of height to shadow length is the same for both the tree and the tower, we can set up the proportion \(\frac{\text{height of tree}}{\text{shadow length of tree}}=\frac{\text{height of tower}}{\text{shadow length of tower}}\). Let \(h\) be the height of the tower. So, \(\frac{12}{9}=\frac{h}{12}\).

Step2: Solve for \(h\)

Cross - multiply: \(9h = 12\times12\). Then \(9h=144\). Divide both sides by 9: \(h=\frac{144}{9}\).

Answer:

16