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Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 75RE
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Use law of cosine or law of sines
**Isosceles Triangle with Angled Measures and Side Length** In the diagram, we have an isosceles triangle. An isosceles triangle is characterized by having at least two sides of equal length. This diagram specifically shows one angle measure and one side length: 1. The triangle has one angle measured at 30 degrees located at the base. 2. The base of the triangle is labeled with a length of 30 units. 3. The two lines extending from the base meet at the top vertex and are marked with a single line each, denoting that these two sides are of equal length. This notation establishes that the two sides opposite the 30-degree angle are equal in length, confirming the property of the triangle being isosceles. **Educational Explanation:** Isosceles triangles are important in geometry due to their symmetrical properties. One key property is that the angles opposite the equal sides are also equal. Hence, if one angle is known (like 30 degrees here), it helps in understanding and solving for the other angles and side lengths based on geometric principles. In this case, knowing the angles and sides inform us of the specific calculations and relationships between each part of the triangle, which can be critical for various applications and further mathematical problems.
Transcribed Image Text:**Isosceles Triangle with Angled Measures and Side Length** In the diagram, we have an isosceles triangle. An isosceles triangle is characterized by having at least two sides of equal length. This diagram specifically shows one angle measure and one side length: 1. The triangle has one angle measured at 30 degrees located at the base. 2. The base of the triangle is labeled with a length of 30 units. 3. The two lines extending from the base meet at the top vertex and are marked with a single line each, denoting that these two sides are of equal length. This notation establishes that the two sides opposite the 30-degree angle are equal in length, confirming the property of the triangle being isosceles. **Educational Explanation:** Isosceles triangles are important in geometry due to their symmetrical properties. One key property is that the angles opposite the equal sides are also equal. Hence, if one angle is known (like 30 degrees here), it helps in understanding and solving for the other angles and side lengths based on geometric principles. In this case, knowing the angles and sides inform us of the specific calculations and relationships between each part of the triangle, which can be critical for various applications and further mathematical problems.
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