What are the missing sides in the triangle written as integers or as decimals rounded to the nearest tenth? The figure is not drawn to scale.A. x=18; y=15.6B. 12.7; y=15.6C. x=12.7; y=9D. x=9; y=12.7 This image depicts a right-angled triangle with one of its other angles measuring 45 degrees. The lengths of the sides of the triangle are labeled as follows:- The side opposite to the right angle is labeled as \( 9 \).- The side adjacent to the 45-degree angle is labeled as \( y \).- The hypotenuse is labeled as \( x \).In a right-angled triangle where one of the angles is 45 degrees, we can use trigonometric identities to solve for the unknown sides. Specifically, in a 45-45-90 triangle, both the legs opposite the 45-degree angles are equal in length.Using the Pythagorean theorem (\( a^2 + b^2 = c^2 \)), we can express the relationships between the sides as follows:1. \( x \) (hypotenuse) = \( 9 \times \sqrt{2} \)2. \( y \) = \( x \times \sin(45°) \)Given the properties of the 45-45-90 triangle:- \( y \) and 9 are the same length.Thus, the hypotenuse can be calculated as:\[ x = 9\sqrt{2} \approx 12.73 \]The diagram helps visualize these relationships and provides a basis for solving problems related to right-angle triangles, especially those involving a 45-degree angle.

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Answered: What are the missing sides in the…

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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What are the missing sides in the triangle written as integers or as decimals rounded to the nearest tenth? The figure is not drawn to scale.

A. x=18; y=15.6

B. 12.7; y=15.6

C. x=12.7; y=9

D. x=9; y=12.7

This image depicts a right-angled triangle with one of its other angles measuring 45 degrees. The lengths of the sides of the triangle are labeled as follows:

- The side opposite to the right angle is labeled as \( 9 \).
- The side adjacent to the 45-degree angle is labeled as \( y \).
- The hypotenuse is labeled as \( x \).

In a right-angled triangle where one of the angles is 45 degrees, we can use trigonometric identities to solve for the unknown sides. Specifically, in a 45-45-90 triangle, both the legs opposite the 45-degree angles are equal in length.

Using the Pythagorean theorem (\( a^2 + b^2 = c^2 \)), we can express the relationships between the sides as follows:

1. \( x \) (hypotenuse) = \( 9 \times \sqrt{2} \)
2. \( y \) = \( x \times \sin(45°) \)

Given the properties of the 45-45-90 triangle:
- \( y \) and 9 are the same length.

Thus, the hypotenuse can be calculated as:
\[ x = 9\sqrt{2} \approx 12.73 \]

The diagram helps visualize these relationships and provides a basis for solving problems related to right-angle triangles, especially those involving a 45-degree angle.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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