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Part A - Finding the length of the hypotenuse of the first triangle For the first triangle, what is the length of its hypotenuse? Express your answer to three significant figures. ► View Available Hint(s)

Part A - Finding the length of the hypotenuse of the first triangle For the first triangle, what is the length of its hypotenuse? Express your answer to three significant figures. ► View Available Hint(s)

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a right triangle with W=27.5 and H=14.0

### Part A - Finding the length of the hypotenuse of the first triangle For the first triangle, what is the length of its hypotenuse? **Express your answer to three significant figures.** #### View Available Hint(s) [Input Box for Answer] \[ X = \, \_\_ \] [Submit Button] --- ### Part B - Finding angle α in the first triangle For the first triangle, what is the value of α? **Express your answer to three significant figures in degrees.** #### View Available Hint(s) [Input Box for Answer] \[ \alpha = \, \_\_ \] [Submit Button] --- ### Explanation of Features: - **Hint Section:** Clicking on "View Available Hint(s)" will provide additional information or strategies to solve the problem. - **Input Box:** This is where students can type their answers. - **Submission Button:** After inputting the answer, students can click "Submit" to record their answer. ### Important Notes: - Be sure to express your answers to three significant figures. - Angle α should be provided in degrees.
Transcribed Image Text:### Part A - Finding the length of the hypotenuse of the first triangle For the first triangle, what is the length of its hypotenuse? **Express your answer to three significant figures.** #### View Available Hint(s) [Input Box for Answer] \[ X = \, \_\_ \] [Submit Button] --- ### Part B - Finding angle α in the first triangle For the first triangle, what is the value of α? **Express your answer to three significant figures in degrees.** #### View Available Hint(s) [Input Box for Answer] \[ \alpha = \, \_\_ \] [Submit Button] --- ### Explanation of Features: - **Hint Section:** Clicking on "View Available Hint(s)" will provide additional information or strategies to solve the problem. - **Input Box:** This is where students can type their answers. - **Submission Button:** After inputting the answer, students can click "Submit" to record their answer. ### Important Notes: - Be sure to express your answers to three significant figures. - Angle α should be provided in degrees.
The image depicts a right-angled triangle, which is a fundamental geometric figure used frequently in trigonometry and geometry. Here’s a detailed description of the components of the triangle as shown: 1. **Sides of the Triangle**: - **X**: This represents the hypotenuse of the triangle, which is the side opposite the right angle. - **H**: This denotes the height (or the opposite side) of the triangle relative to the angle \( \alpha \). - **W**: This signifies the base (or the adjacent side) of the triangle relative to the angle \( \alpha \). 2. **Angle**: - **\( \alpha \)**: This is the acute angle situated between side \( W \) (the base) and the hypotenuse \( X \). 3. **Right Angle**: - The triangle has one right angle, which is marked by a small square at the intersection of sides \( W \) and \( H \). This diagram can be used to explain various trigonometric concepts such as sine, cosine, and tangent. For instance: - **Sine of \( \alpha \)**: \( \sin(\alpha) = \frac{H}{X} \) - **Cosine of \( \alpha \)**: \( \cos(\alpha) = \frac{W}{X} \) - **Tangent of \( \alpha \)**: \( \tan(\alpha) = \frac{H}{W} \) Understanding these relationships is crucial for solving problems related to right-angled triangles, and it can also be extended to various applications in physics, engineering, and other fields involving spatial analysis.
Transcribed Image Text:The image depicts a right-angled triangle, which is a fundamental geometric figure used frequently in trigonometry and geometry. Here’s a detailed description of the components of the triangle as shown: 1. **Sides of the Triangle**: - **X**: This represents the hypotenuse of the triangle, which is the side opposite the right angle. - **H**: This denotes the height (or the opposite side) of the triangle relative to the angle \( \alpha \). - **W**: This signifies the base (or the adjacent side) of the triangle relative to the angle \( \alpha \). 2. **Angle**: - **\( \alpha \)**: This is the acute angle situated between side \( W \) (the base) and the hypotenuse \( X \). 3. **Right Angle**: - The triangle has one right angle, which is marked by a small square at the intersection of sides \( W \) and \( H \). This diagram can be used to explain various trigonometric concepts such as sine, cosine, and tangent. For instance: - **Sine of \( \alpha \)**: \( \sin(\alpha) = \frac{H}{X} \) - **Cosine of \( \alpha \)**: \( \cos(\alpha) = \frac{W}{X} \) - **Tangent of \( \alpha \)**: \( \tan(\alpha) = \frac{H}{W} \) Understanding these relationships is crucial for solving problems related to right-angled triangles, and it can also be extended to various applications in physics, engineering, and other fields involving spatial analysis.
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