The following equation about triangle ABC is true. Select all possible representations of ABC. sin [ 40° ] = b/c ### Triangle Trigonometry Problem#### Problem Statement:The following equation about triangle ABC is true. Select all possible representations of ABC. \[ \sin(40^\circ) = \frac{b}{c} \]#### Options:1. **Option 1:** - Right triangle with vertices labeled $ A $, $ B $, and $ C $. - Angle $ CAB = 90^\circ $. - Angle $ BCA = 40^\circ $. - Side opposite to $ 40^\circ $ (side $ a $) is labeled. - Side opposite to $ 90^\circ $ (hypotenuse $ c $) is labeled. - Side adjacent to $ 40^\circ $ (side $ b $) is labeled.2. **Option 2:** - Triangle with vertices labeled $ A $, $ B $, and $ C $. - Angle $ BAC = 40^\circ $. - Side opposite to $ 40^\circ $ (side $ b $) is labeled. - Side adjacent to $ 40^\circ $ (side $ a $) is labeled. - Side opposite to angle $ A $ (side $ c $) is labeled.3. **Option 3:** - Right triangle with vertices labeled $ A $, $ B $, and $ C $. - Angle $ BCA = 40^\circ $. - Angle $ ACB = 90^\circ $. - Side opposite to $ B = 40^\circ $ (side $ a $) is labeled. - Side opposite to $ C = 90^\circ $ (hypotenuse $ c $) is labeled. - Side adjacent to $ 40^\circ $ (side $ b $) is labeled.4. **Option 4:** - Triangle with vertices labeled $ A $, $ B $, and $ C $. - Angle $ BAC = 50^\circ $ indicated. - Side opposite to $ 50^\circ $ (side $ a $) is labeled. - Remaining sides are labeled as $ b $ (opposite to $ C $) and $ c $ (opposite to $ B $).#### Analysis:To have \( \sin(40^\circ) = \ The image presents a right-angled triangle with vertices labeled A, B, and C. Vertex C is the right angle (90°), and the angles at vertices A and B are marked as follows:- Angle BCA (vertex C angle) is 90°.- Angle ABC (vertex B angle) is 50°.- Angle BAC (vertex A angle) can be calculated as 40° because the sum of the angles in a triangle is always 180° (180° - 90° - 50° = 40°).The sides of the triangle are labeled with lowercase letters corresponding to the vertices opposite them:- Side a: The side opposite angle BAC, connecting points A and B.- Side b: The side opposite angle ABC, connecting points A and C.- Side c: The hypotenuse opposite the right angle, connecting points B and C.Under the image is a checkbox labeled "Option 5." There are no other options visible in the provided image.

Sine is a trigonometric function which is defined as the ratio of side opposite to a angle in a…

Answered: The following equation about triangle…

Elementary Geometry For College Students, 7e

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ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

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The following equation about triangle ABC is true. Select all possible representations of ABC. sin [ 40° ] = b/c

### Triangle Trigonometry Problem

#### Problem Statement:
The following equation about triangle ABC is true. Select all possible representations of ABC.
\[ \sin(40^\circ) = \frac{b}{c} \]

#### Options:

1. **Option 1:**
- Right triangle with vertices labeled $ A $, $ B $, and $ C $.
- Angle $ CAB = 90^\circ $.
- Angle $ BCA = 40^\circ $.
- Side opposite to $ 40^\circ $ (side $ a $) is labeled.
- Side opposite to $ 90^\circ $ (hypotenuse $ c $) is labeled.
- Side adjacent to $ 40^\circ $ (side $ b $) is labeled.

2. **Option 2:**
- Triangle with vertices labeled $ A $, $ B $, and $ C $.
- Angle $ BAC = 40^\circ $.
- Side opposite to $ 40^\circ $ (side $ b $) is labeled.
- Side adjacent to $ 40^\circ $ (side $ a $) is labeled.
- Side opposite to angle $ A $ (side $ c $) is labeled.

3. **Option 3:**
- Right triangle with vertices labeled $ A $, $ B $, and $ C $.
- Angle $ BCA = 40^\circ $.
- Angle $ ACB = 90^\circ $.
- Side opposite to $ B = 40^\circ $ (side $ a $) is labeled.
- Side opposite to $ C = 90^\circ $ (hypotenuse $ c $) is labeled.
- Side adjacent to $ 40^\circ $ (side $ b $) is labeled.

4. **Option 4:**
- Triangle with vertices labeled $ A $, $ B $, and $ C $.
- Angle $ BAC = 50^\circ $ indicated.
- Side opposite to $ 50^\circ $ (side $ a $) is labeled.
- Remaining sides are labeled as $ b $ (opposite to $ C $) and $ c $ (opposite to $ B $).

#### Analysis:
To have \( \sin(40^\circ) = \

The image presents a right-angled triangle with vertices labeled A, B, and C. Vertex C is the right angle (90°), and the angles at vertices A and B are marked as follows:
- Angle BCA (vertex C angle) is 90°.
- Angle ABC (vertex B angle) is 50°.
- Angle BAC (vertex A angle) can be calculated as 40° because the sum of the angles in a triangle is always 180° (180° - 90° - 50° = 40°).

The sides of the triangle are labeled with lowercase letters corresponding to the vertices opposite them:
- Side a: The side opposite angle BAC, connecting points A and B.
- Side b: The side opposite angle ABC, connecting points A and C.
- Side c: The hypotenuse opposite the right angle, connecting points B and C.

Under the image is a checkbox labeled "Option 5." There are no other options visible in the provided image.

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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