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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### Geometry Problem: Determining the Measure of Angle C **Problem Description:** What is the measure of Angle C? (Round to the nearest tenth) **Instructions:** To find the measure of Angle C, you might need to use geometric principles such as the angle sum of a triangle or trigonometric functions. Ensure your final answer is rounded to the nearest tenth. **Notes:** 1. If you are given a triangle, the sum of the internal angles is always 180 degrees. 2. Trigonometric functions such as sine, cosine, and tangent may be helpful depending on the information provided (sides and/or other angles). For illustrative purposes, if a diagram of a triangle or other geometrical figure is part of this problem, observe any given side lengths or angles as they can provide significant guidance for solving the problem.
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Transcribed Image Text:### Geometry Problem: Determining the Measure of Angle C **Problem Description:** What is the measure of Angle C? (Round to the nearest tenth) **Instructions:** To find the measure of Angle C, you might need to use geometric principles such as the angle sum of a triangle or trigonometric functions. Ensure your final answer is rounded to the nearest tenth. **Notes:** 1. If you are given a triangle, the sum of the internal angles is always 180 degrees. 2. Trigonometric functions such as sine, cosine, and tangent may be helpful depending on the information provided (sides and/or other angles). For illustrative purposes, if a diagram of a triangle or other geometrical figure is part of this problem, observe any given side lengths or angles as they can provide significant guidance for solving the problem.
### Right Triangle ABC The image depicts a right triangle labeled as triangle ABC where angle B is the right angle (90 degrees). Here are the details of the sides: - **Side \(AB\)**: This is one of the two legs forming the right angle. It is perpendicular to side \(BC\). - **Side \(BC\)**: This is the other leg forming the right angle at B. The length of side \(BC\) is labeled as 24 units. - **Side \(AC\)**: This is the hypotenuse of the right triangle, which is the side opposite the right angle. The length of the hypotenuse is labeled as 25 units. The right angle at point B is indicated with a small square in the corner. ### Explanation In the context of right triangles, the lengths of the sides are often related according to the Pythagorean theorem. The theorem states that in a right-angled triangle: \[ \text{(Length of Hypotenuse)}^2 = \text{(Length of one leg)}^2 + \text{(Length of other leg)}^2 \] In this diagram, the hypotenuse \(AC\) is labeled 25, and one of the legs \(BC\) is labeled 24. To find the length of the other leg \(AB\), you would perform the following calculation: \[ AC^2 = AB^2 + BC^2 \] \[ 25^2 = AB^2 + 24^2 \] \[ 625 = AB^2 + 576 \] \[ AB^2 = 625 - 576 \] \[ AB^2 = 49 \] \[ AB = \sqrt{49} \] \[ AB = 7 \] Therefore, the length of side \(AB\) is 7 units.
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Transcribed Image Text:### Right Triangle ABC The image depicts a right triangle labeled as triangle ABC where angle B is the right angle (90 degrees). Here are the details of the sides: - **Side \(AB\)**: This is one of the two legs forming the right angle. It is perpendicular to side \(BC\). - **Side \(BC\)**: This is the other leg forming the right angle at B. The length of side \(BC\) is labeled as 24 units. - **Side \(AC\)**: This is the hypotenuse of the right triangle, which is the side opposite the right angle. The length of the hypotenuse is labeled as 25 units. The right angle at point B is indicated with a small square in the corner. ### Explanation In the context of right triangles, the lengths of the sides are often related according to the Pythagorean theorem. The theorem states that in a right-angled triangle: \[ \text{(Length of Hypotenuse)}^2 = \text{(Length of one leg)}^2 + \text{(Length of other leg)}^2 \] In this diagram, the hypotenuse \(AC\) is labeled 25, and one of the legs \(BC\) is labeled 24. To find the length of the other leg \(AB\), you would perform the following calculation: \[ AC^2 = AB^2 + BC^2 \] \[ 25^2 = AB^2 + 24^2 \] \[ 625 = AB^2 + 576 \] \[ AB^2 = 625 - 576 \] \[ AB^2 = 49 \] \[ AB = \sqrt{49} \] \[ AB = 7 \] Therefore, the length of side \(AB\) is 7 units.
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