Question

multiple choice (single... as shown below, a tree breaks at a height of 3 m above the ground. the top part of the tree falls and lands 4 m away from the base of the trunk. what was the total height of the tree before it broke? a 5 m b 12 m c 8 m d 5 m or 7 m

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the broken part of the tree be \(l\). The broken part, the remaining part of the tree (\(3m\)), and the distance on the ground (\(4m\)) form a right - triangle. By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 3\), \(b=4\), and \(c=l\). So \(l=\sqrt{3^{2}+4^{2}}\).

Step2: Calculate the length of the broken part

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Step3: Calculate the total height of the tree

The total height of the tree \(H\) is the sum of the remaining part (\(3m\)) and the broken part (\(l = 5m\)). So \(H=3 + 5\).

Answer:

C. \(8m\)