hello, can you help me with this?What is the area of triangle XYZtriangle XYZ to the nearest tenth of a square inch? Use special right triangles to help find the height. Leave your answer in terms of the radical. "Show your work." please The image displays a right-angled triangle labeled XYZ.- The right angle is located at vertex X.- The horizontal side, XZ, which is the base of the triangle, has a length of 12 feet.- Angle YXZ is 60 degrees.- The vertical side, XY, and the hypotenuse, YZ, are also shown but their lengths are not provided.Such a triangle is commonly studied in trigonometry and geometry, where you may need to find unknown side lengths or angles using trigonometric ratios and the Pythagorean theorem. This triangle appears to be a 30-60-90 triangle, a special type of right-angled triangle that has side ratios of 1 : √3 : 2. In this case, since angle XYZ is 30 degrees and angle YXZ is 60 degrees, the leg opposite the 30-degree angle (XZ) is half the hypotenuse (YZ), and the leg opposite the 60-degree angle (XY) is √3 times the shorter leg (XZ). Given that XZ is 12 feet, XY will be 12√3 feet, and YZ, the hypotenuse, will be 24 feet. This is a foundational concept in trigonometry, illustrating the relationship between the angles and side lengths in right-angled triangles.

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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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hello, can you help me with this?

What is the area of triangle XYZtriangle XYZ to the nearest tenth of a square inch? Use special right triangles to help find the height. Leave your answer in terms of the radical.

"Show your work." please

The image displays a right-angled triangle labeled XYZ.

- The right angle is located at vertex X.
- The horizontal side, XZ, which is the base of the triangle, has a length of 12 feet.
- Angle YXZ is 60 degrees.
- The vertical side, XY, and the hypotenuse, YZ, are also shown but their lengths are not provided.

Such a triangle is commonly studied in trigonometry and geometry, where you may need to find unknown side lengths or angles using trigonometric ratios and the Pythagorean theorem. This triangle appears to be a 30-60-90 triangle, a special type of right-angled triangle that has side ratios of 1 : √3 : 2.

In this case, since angle XYZ is 30 degrees and angle YXZ is 60 degrees, the leg opposite the 30-degree angle (XZ) is half the hypotenuse (YZ), and the leg opposite the 60-degree angle (XY) is √3 times the shorter leg (XZ). Given that XZ is 12 feet, XY will be 12√3 feet, and YZ, the hypotenuse, will be 24 feet.

This is a foundational concept in trigonometry, illustrating the relationship between the angles and side lengths in right-angled triangles.

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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