Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question
**Instructions: Find the value of x and y in each triangle.** 1. **Triangle 1** - Given: A right triangle with angles 60° and a right angle. - Sides: One side marked as 8 (adjacent to the right angle) and the other sides labeled as x and y. 2. **Triangle 2** - Given: A right triangle with angles 60°, 30°, and a right angle. - Sides: The shorter leg opposite the 30° angle is marked as 1/2. The hypotenuse is labeled as x, and the other leg (adjacent to the 30° angle) is labeled as y. 3. **Triangle 3** - Given: A right triangle with angles 30° and a right angle. - Sides: The hypotenuse is marked as 14, with the other sides labeled x (opposite the 30° angle) and y. **Explanation for Solving:** To find the values of x and y in these right triangles, one can use trigonometric ratios or specific properties of 30°-60°-90° triangles: - In a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. For example, the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is the shorter leg times √3. - Use these properties, along with the Pythagorean theorem if needed, to find the unknown sides.
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Transcribed Image Text:**Instructions: Find the value of x and y in each triangle.** 1. **Triangle 1** - Given: A right triangle with angles 60° and a right angle. - Sides: One side marked as 8 (adjacent to the right angle) and the other sides labeled as x and y. 2. **Triangle 2** - Given: A right triangle with angles 60°, 30°, and a right angle. - Sides: The shorter leg opposite the 30° angle is marked as 1/2. The hypotenuse is labeled as x, and the other leg (adjacent to the 30° angle) is labeled as y. 3. **Triangle 3** - Given: A right triangle with angles 30° and a right angle. - Sides: The hypotenuse is marked as 14, with the other sides labeled x (opposite the 30° angle) and y. **Explanation for Solving:** To find the values of x and y in these right triangles, one can use trigonometric ratios or specific properties of 30°-60°-90° triangles: - In a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. For example, the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is the shorter leg times √3. - Use these properties, along with the Pythagorean theorem if needed, to find the unknown sides.
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