Question

Following Hurricane Katrina in 2005, thousands of pine trees in southeastern Louisiana formed right triangles as shown in the photo. Suppose that, for a small such tree, the vertical distance from the base of the broken tree to the point of the break is 4.5 ft. The length of the broken part is 12 ft. How far along the ground is it from the base of the tree to the point where the broken part (IMAGE CANT COPY) touches the ground?

Name: Problem 77, Chapter 8: Beginning Algebra
Uploaded: 2020-06-30T19:06:49-08:00
Duration: 1 min 36 s
Channel: Melissa Stefan

   Following Hurricane Katrina in 2005, thousands of pine trees in southeastern Louisiana formed right triangles as shown in the photo. Suppose that, for a small such tree, the vertical distance from the base of the broken tree to the point of the break is 4.5 ft. The length of
the broken part is 12 ft. How far along the ground is it from the base of the tree to the point where the broken part 
(IMAGE CANT COPY)
touches the ground?

Beginning Algebra

Margaret L. Lial,… 11th Edition

Chapter 8, Problem 77

Instant Answer

Solved by Expert Melissa Stefan

06/30/2020

Step 1

5 ft (which we can consider as one of the sides of the triangle) and the length of the broken part is 12 ft (which we can consider as the hypotenuse of the triangle). We are asked to find the horizontal distance from the base of the tree to the point where the Show more…

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Following Hurricane Katrina in 2005, thousands of pine trees in southeastern Louisiana formed right triangles as shown in the photo. Suppose that, for a small such tree, the vertical distance from the base of the broken tree to the point of the break is 4.5 ft. The length of the broken part is 12 ft. How far along the ground is it from the base of the tree to the point where the broken part (IMAGE CANT COPY) touches the ground?

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Key Concepts

Pythagorean Theorem

This theorem is fundamental in geometry and states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It is essential for calculating unknown side lengths when two sides of a right triangle are known.

Right Triangle

A right triangle has one angle of 90 degrees. The properties of right triangles, especially the relationship between their side lengths as described by the Pythagorean theorem, are crucial in solving problems involving distances and heights.

Application of Square Roots

Once the relationship between the sides is established (using the squared terms), calculating the exact length of a side often involves taking a square root. This process is a key algebraic step in transitioning from squared values back to the original measurements.

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