Textbook Question
Find the unknown side lengths in each pair of similar triangles.
Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 2, Problem 21
In each figure, there are two similar triangles. Find the unknown measurement. Give any approximation to the nearest tenth.
Verified step by step guidance1
Identify the corresponding sides of the two similar triangles. Since the triangles are similar, their corresponding sides are proportional.
Set up a proportion equation using the lengths of the known sides and the unknown side. For example, if the sides correspond as \(a\) to \(a'\), \(b\) to \(b'\), and \(c\) to \(c'\), then the ratio \(\frac{a}{a'} = \frac{b}{b'} = \frac{c}{c'}\) holds.
Choose the pair of corresponding sides where you know three of the lengths (two from one triangle and one from the other) to form an equation with the unknown side.
Solve the proportion equation for the unknown side by cross-multiplying and isolating the variable.
Once you find the value of the unknown side, round your answer to the nearest tenth as requested.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Similarity of Triangles
Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. This means one triangle is a scaled version of the other, allowing us to set up ratios between corresponding sides to find unknown lengths.
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Proportionality of Corresponding Sides
In similar triangles, the ratios of the lengths of corresponding sides are equal. This property enables solving for unknown side lengths by setting up and solving proportion equations based on known side measurements.
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Rounding and Approximation
When calculating unknown measurements, the result may be an irrational or decimal number. Rounding to the nearest tenth means adjusting the value to one decimal place, which simplifies the answer while maintaining reasonable accuracy.
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Related Practice
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