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Find the measure of the indicated angle to the nearest degree. 9) 9 ?/ A) 39° B) 35° C) 51° D) 55° The polygons in each pair are similar. Find the missing side 11

Find the measure of the indicated angle to the nearest degree. 9) 9 ?/ A) 39° B) 35° C) 51° D) 55° The polygons in each pair are similar. Find the missing side 11

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Find the Measure of the Indicated Angle to the Nearest Degree** Given the triangle shown below, determine the measure of the angle marked with a question mark. The known side lengths of the triangle are provided as follows: - The side opposite the right angle is marked as 9. - The adjacent side to the angle in question is marked as 11. Below are the possible answers: - A) \(39^\circ\) - B) \(35^\circ\) - C) \(51^\circ\) - D) \(55^\circ\) **Figure Details** The triangle illustrated is a right-angled triangle with one of the non-right angles described, and the side lengths given. - The hypotenuse (side opposite the right angle) is 9. - One of the other sides adjacent to the angle in question is 11. - The right angle (indicated by a small square at the corner) conforms to the standard notation for specifying right angles in mathematical diagrams. To determine the measure of the indicated angle, you can utilize trigonometric ratios, particularly the tangent function in this case: \[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \] Where: - The opposite side is 9 - The adjacent side is 11 Therefore: \[ \theta = \tan^{-1}\left(\frac{9}{11}\right) \] **Educational Note** Understanding and calculating angles in a right-angled triangle is an integral part of trigonometry and geometry. This problem is an application of basic trigonometric functions to find unknown angles, which is a crucial skill in various fields including mathematics, physics, engineering, and architecture. Practicing these types of problems helps solidify the concepts of trigonometric ratios and the relationships between triangle sides and their angles.
Transcribed Image Text:**Find the Measure of the Indicated Angle to the Nearest Degree** Given the triangle shown below, determine the measure of the angle marked with a question mark. The known side lengths of the triangle are provided as follows: - The side opposite the right angle is marked as 9. - The adjacent side to the angle in question is marked as 11. Below are the possible answers: - A) \(39^\circ\) - B) \(35^\circ\) - C) \(51^\circ\) - D) \(55^\circ\) **Figure Details** The triangle illustrated is a right-angled triangle with one of the non-right angles described, and the side lengths given. - The hypotenuse (side opposite the right angle) is 9. - One of the other sides adjacent to the angle in question is 11. - The right angle (indicated by a small square at the corner) conforms to the standard notation for specifying right angles in mathematical diagrams. To determine the measure of the indicated angle, you can utilize trigonometric ratios, particularly the tangent function in this case: \[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \] Where: - The opposite side is 9 - The adjacent side is 11 Therefore: \[ \theta = \tan^{-1}\left(\frac{9}{11}\right) \] **Educational Note** Understanding and calculating angles in a right-angled triangle is an integral part of trigonometry and geometry. This problem is an application of basic trigonometric functions to find unknown angles, which is a crucial skill in various fields including mathematics, physics, engineering, and architecture. Practicing these types of problems helps solidify the concepts of trigonometric ratios and the relationships between triangle sides and their angles.
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