The figures are similar. Find x ### Exploring Similar TrianglesWhen studying geometry, particularly the properties of triangles, a useful concept is that of similar triangles. Triangles are considered similar if their corresponding angles are equal and their corresponding sides are in proportion.**Example Problem: Finding the Unknown Side**Below are two similar right triangles. We'll use the fact that the corresponding sides of similar triangles are proportional to find the unknown side length, \( x \).#### Diagram Explanation:In the image, we have two right triangles:1. The first triangle has sides labeled as 18, \( x \), and an included angle.2. The second triangle has sides labeled as 27, 20, and the same included angle.#### Step-by-Step Solution:1. **Identify Corresponding Sides:** - The triangle with sides 18 and \( x \) is similar to the triangle with sides 27 and 20. - This similarity sets up a proportion between the corresponding sides of the two triangles.2. **Set Up Proportions:** - By the property of similar triangles: \[ \frac{18}{27} = \frac{x}{20} \]3. **Solve for \( x \):** - Simplify the proportion: \[ \frac{18}{27} = \frac{2}{3} \] - Now, write the proportion from the similar triangles: \[ \frac{2}{3} = \frac{x}{20} \] - Cross-multiply to solve for \( x \): \[ 2 \cdot 20 = 3 \cdot x \implies 40 = 3x \implies x = \frac{40}{3} \implies x = 13.\overline{3} \]Therefore, the length of the side \( x \) in the first triangle is approximately \( 13.\overline{3} \).Understanding the principle of similar triangles and the method of setting up proportions is crucial in solving these kinds of geometric problems. It allows you to find missing lengths and understand the relationships between different parts of geometric figures.

Two given triangles are similar. We have to find x. We know that the corresponding sides of similar…

Answered: The figures are similar. Find x

Math

Algebra

The figures are similar. Find x

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter9: Real Numbers And Right Triangles

Section9.7: The Tangent Ration

Problem 29E

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