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In a 90°-30°-60° triangle, the shortest leg is half of the hypotenuse. True False

In a 90°-30°-60° triangle, the shortest leg is half of the hypotenuse. True False

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
**Understanding 30-60-90 Triangles: Educational Insight** **Question:** In a 90°-30°-60° triangle, the shortest leg is half of the hypotenuse. - **True**: ⭕ - **False**: ⭕ A 30-60-90 triangle is a special type of right triangle where the angles are specifically 30 degrees, 60 degrees, and 90 degrees. One unique property of this triangle is the ratio of the lengths of its sides. The shortest side, opposite the 30-degree angle, is always half the length of the hypotenuse. The side opposite the 60-degree angle is equal to the shortest side times the square root of three. In a more visual context, if you imagine a 30-60-90 triangle with the hypotenuse being twice the shortest side, it becomes evident that the shortest leg is indeed one-half the hypotenuse. Validation of this question helps reinforce the understanding of the relationships within these special right triangles, crucial for geometry and trigonometry learners. **Diagram Explanation:** Unfortunately, no diagram is included with this material, but consider the following to visualize: - If the shortest leg (opposite 30° angle) is 'x', then: - The hypotenuse (opposite 90° angle) is '2x'. - The longer leg (opposite 60° angle) is 'x√3'. Such ratios simplify solving problems involving right triangles with these specific angles.
Transcribed Image Text:**Understanding 30-60-90 Triangles: Educational Insight** **Question:** In a 90°-30°-60° triangle, the shortest leg is half of the hypotenuse. - **True**: ⭕ - **False**: ⭕ A 30-60-90 triangle is a special type of right triangle where the angles are specifically 30 degrees, 60 degrees, and 90 degrees. One unique property of this triangle is the ratio of the lengths of its sides. The shortest side, opposite the 30-degree angle, is always half the length of the hypotenuse. The side opposite the 60-degree angle is equal to the shortest side times the square root of three. In a more visual context, if you imagine a 30-60-90 triangle with the hypotenuse being twice the shortest side, it becomes evident that the shortest leg is indeed one-half the hypotenuse. Validation of this question helps reinforce the understanding of the relationships within these special right triangles, crucial for geometry and trigonometry learners. **Diagram Explanation:** Unfortunately, no diagram is included with this material, but consider the following to visualize: - If the shortest leg (opposite 30° angle) is 'x', then: - The hypotenuse (opposite 90° angle) is '2x'. - The longer leg (opposite 60° angle) is 'x√3'. Such ratios simplify solving problems involving right triangles with these specific angles.
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