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Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Trigonometry
Section1.8: Applications And Models
Problem 4ECP: From the time a small airplane is 100 feet high and 1600 ground feet from its landing runway, the...
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Find the values of X and Y in the right triangle.

This image illustrates a right triangle with a given side length and angle measurement. The components of the triangle are labeled as follows: - \( y \) represents the hypotenuse of the triangle. - \( x \) represents the other leg of the triangle. - The given side length adjacent to the 60-degree angle is \( 12\sqrt{3} \). The angle opposite the side \( 12\sqrt{3} \) is \( 60^\circ \), and the right angle (90 degrees) is denoted by the small square at the corner of the triangle. This triangle can be analyzed using trigonometric principles. Because it includes a 60-degree angle, it is a 30-60-90 triangle. In such triangles, the ratios between the lengths of the sides are always consistent. Specifically: - The side opposite the 30-degree angle is \( s \). - The side opposite the 60-degree angle is \( s\sqrt{3} \). - The hypotenuse is \( 2s \). Given the side length \( 12\sqrt{3} \) opposite the 60-degree angle, we can find the other sides using these ratios.
Transcribed Image Text:This image illustrates a right triangle with a given side length and angle measurement. The components of the triangle are labeled as follows: - \( y \) represents the hypotenuse of the triangle. - \( x \) represents the other leg of the triangle. - The given side length adjacent to the 60-degree angle is \( 12\sqrt{3} \). The angle opposite the side \( 12\sqrt{3} \) is \( 60^\circ \), and the right angle (90 degrees) is denoted by the small square at the corner of the triangle. This triangle can be analyzed using trigonometric principles. Because it includes a 60-degree angle, it is a 30-60-90 triangle. In such triangles, the ratios between the lengths of the sides are always consistent. Specifically: - The side opposite the 30-degree angle is \( s \). - The side opposite the 60-degree angle is \( s\sqrt{3} \). - The hypotenuse is \( 2s \). Given the side length \( 12\sqrt{3} \) opposite the 60-degree angle, we can find the other sides using these ratios.
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