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To estimate the height of a tree, a forester uses the concept of similar triangles. A particular tree is found to have a shadow measuring 84 feet in length. The forester has her own shadow measured at the same time. Her shadow measures $7 \frac{1}{2}$ feet. If she is $5 \frac{1}{2}$ feet tall, how tall is the tree? (FIGURE CAN'T COPY).

Name: Problem 49, Chapter 7: Prealgebra
Uploaded: 2020-05-05T18:24:22-08:00
Duration: 36 s
Channel: Ali Soave
Description: To estimate the height of a tree, a forester uses the concept of similar triangles. A particular tree is found to have a shadow measuring 84 feet in length. The forester has her own shadow measured at the same time. Her shadow measures 7 (1)/(2) feet. If she is 5 (1)/(2) feet tall, how tall is the tree? (FIGURE CAN'T COPY).

   To estimate the height of a tree, a forester uses the concept of similar triangles. A particular tree is found to have a shadow measuring 84 feet in length. The forester has her own shadow measured at the same time. Her shadow measures $7 \frac{1}{2}$ feet. If she is $5 \frac{1}{2}$ feet tall, how tall is the tree? (FIGURE CAN'T COPY).

Prealgebra

Tom Carson 4th Edition

Chapter 7, Problem 49

Instant Answer

Solved by Expert Ali Soave

05/05/2020

Step 1

The height of the forester is to her shadow as the height of the tree is to its shadow. This can be written as: \[\frac{5.5}{7.5} = \frac{x}{84}\] Show more…

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To estimate the height of a tree, a forester uses the concept of similar triangles. A particular tree is found to have a shadow measuring 84 feet in length. The forester has her own shadow measured at the same time. Her shadow measures $7 \frac{1}{2}$ feet. If she is $5 \frac{1}{2}$ feet tall, how tall is the tree? (FIGURE CAN'T COPY).

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Key Concepts

Similar Triangles

Similar triangles are triangles that have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are in proportion. This concept allows one to apply the idea of proportionality to determine unknown lengths or heights when direct measurement is impractical.

Proportional Reasoning

Proportional reasoning involves setting up and solving equations based on the equivalence of ratios. In geometric problems, when figures are similar, the ratio of one pair of corresponding sides is equal to the ratio of any other pair, allowing for the computation of unknown measurements.

Scale Factor

The scale factor is the constant multiplier that relates the lengths of corresponding sides in similar figures. Once this factor is established, it can be applied to convert measurements from a small, known scale to a larger, unknown dimension, facilitating indirect measurements.

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