Find the altitude of this right triangle ### Diagram of a Triangle with Height and Base SegmentsThe image displays a right-angled triangle $ \triangle ABC $ with the following components:1. **Vertices and Sides:** - The triangle consists of vertices labeled $ A $, $ B $, and $ C $. - The sides opposite the vertices are as follows: - $ AB = c $ - $ AC = b $ - $ BC = a $2. **Right Angle:** - The triangle has a right angle (90°) at vertex $ C $.3. **Height:** - The height ($ h $) of the triangle extends from vertex $ C $ to point $ D $ on side $ AB $ such that it is perpendicular to $ AB $. - Height ($ h $) intersects $ AB $ at the right angle (90°), forming the right triangle $ \triangle ACD $.4. **Segment Lengths:** - Segment $ AD $ has a length of $ n = 3 \text{ cm} $. - Segment $ DB $ has a length of $ m = 12 \text{ cm} $. The triangle is a useful illustration for discussing right-angled triangles, height in triangles, and segment lengths in geometry. It's beneficial for comprehending the relationship and properties of the geometrical elements in a right-angled triangle. Additionally, this diagram is useful for applying the Pythagorean Theorem, calculating areas of triangles, and understanding the concept of perpendicular height from a vertex to its opposite side. Key concepts to explore based on this diagram include:- Calculating the lengths of unknown sides using the Pythagorean Theorem.- Determining the height of the triangle.- Finding the areas using base and height measurements.By examining and working through examples like these, one can gain a deeper understanding of fundamental geometric principles.

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Answered: C 90° a. ih n3D3cm1 m%3D12cm 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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Find the altitude of this right triangle

### Diagram of a Triangle with Height and Base Segments

The image displays a right-angled triangle $ \triangle ABC $ with the following components:

1. **Vertices and Sides:**
- The triangle consists of vertices labeled $ A $, $ B $, and $ C $.
- The sides opposite the vertices are as follows:
- $ AB = c $
- $ AC = b $
- $ BC = a $

2. **Right Angle:**
- The triangle has a right angle (90°) at vertex $ C $.

3. **Height:**
- The height ($ h $) of the triangle extends from vertex $ C $ to point $ D $ on side $ AB $ such that it is perpendicular to $ AB $.
- Height ($ h $) intersects $ AB $ at the right angle (90°), forming the right triangle $ \triangle ACD $.

4. **Segment Lengths:**
- Segment $ AD $ has a length of $ n = 3 \text{ cm} $.
- Segment $ DB $ has a length of $ m = 12 \text{ cm} $.

The triangle is a useful illustration for discussing right-angled triangles, height in triangles, and segment lengths in geometry. It's beneficial for comprehending the relationship and properties of the geometrical elements in a right-angled triangle.

Additionally, this diagram is useful for applying the Pythagorean Theorem, calculating areas of triangles, and understanding the concept of perpendicular height from a vertex to its opposite side.

Key concepts to explore based on this diagram include:
- Calculating the lengths of unknown sides using the Pythagorean Theorem.
- Determining the height of the triangle.
- Finding the areas using base and height measurements.

By examining and working through examples like these, one can gain a deeper understanding of fundamental geometric principles.

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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C 90° a. ih n3D3cm1 m%3D12cm the approximate