Right triangle ABC is shown in the xy-plane above. What is the value of tan A ? Please explain, thanks! ### Geometry Problem: Finding the Tangent of Angle $A$In the diagram provided, we have a right triangle $ \triangle ABC $ situated in the $ xy $-plane. The vertices of the triangle are given by the coordinates:- $ A (-5, 4) $- $ B (7, -3) $- $ C (7, 4) $### Problem StatementRight triangle $ \triangle ABC $ is shown in the $ xy $-plane above. What is the value of $ \tan A $?### Options:A) $ \frac{7}{12} $B) $ \frac{3}{4} $C) $ \frac{7}{9} $D) $ \frac{12}{7} $### Explanation of the GraphIn the provided graph:- The x-axis and y-axis intersect at point $ O $ (the origin).- Point $ A $ is located at $(-5, 4)$.- Point $ B $ is located at $(7, -3)$.- Point $ C $ is located at $(7, 4)$.The triangle $ \triangle ABC $ forms a right triangle because:- Line segment $ AC $ is horizontal.- Line segment $ BC $ is vertical.### Finding the Tangent of Angle $ A $To calculate $ \tan A $:- First, determine the lengths of the legs $ AB $ and $ BC $.- The length of $ BC $ is the vertical distance between $ B $ and $ C $, which is: \[ |4 - (-3)| = 7 \]- The length of $ AC $ is the horizontal distance between $ A $ and $ C $, which is: \[ |7 - (-5)| = 12 \]- $ AB $ is the hypotenuse and is not needed to calculate $ \tan A $.The tangent of angle $ A $ is the ratio of the length of the side opposite angle $ A $ (which is $ BC $) to the length of the side adjacent to angle $ A $ (which is $ AC $):\[\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{

The right triangle has coordinates A(-5,4) , B(7,-3) , C(7,4)

Answered: y A(-5,4) C(7,4) В(7,-3) Right triangle…

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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Right triangle ABC is shown in the xy-plane above. What is the value of tan A ? Please explain, thanks!

### Geometry Problem: Finding the Tangent of Angle $A$

In the diagram provided, we have a right triangle $ \triangle ABC $ situated in the $ xy $-plane. The vertices of the triangle are given by the coordinates:
- $ A (-5, 4) $
- $ B (7, -3) $
- $ C (7, 4) $

### Problem Statement

Right triangle $ \triangle ABC $ is shown in the $ xy $-plane above. What is the value of $ \tan A $?

### Options:
A) $ \frac{7}{12} $

B) $ \frac{3}{4} $

C) $ \frac{7}{9} $

D) $ \frac{12}{7} $

### Explanation of the Graph

In the provided graph:
- The x-axis and y-axis intersect at point $ O $ (the origin).
- Point $ A $ is located at $(-5, 4)$.
- Point $ B $ is located at $(7, -3)$.
- Point $ C $ is located at $(7, 4)$.

The triangle $ \triangle ABC $ forms a right triangle because:
- Line segment $ AC $ is horizontal.
- Line segment $ BC $ is vertical.

### Finding the Tangent of Angle $ A $

To calculate $ \tan A $:
- First, determine the lengths of the legs $ AB $ and $ BC $.
- The length of $ BC $ is the vertical distance between $ B $ and $ C $, which is:
\[
|4 - (-3)| = 7
\]
- The length of $ AC $ is the horizontal distance between $ A $ and $ C $, which is:
\[
|7 - (-5)| = 12
\]
- $ AB $ is the hypotenuse and is not needed to calculate $ \tan A $.

The tangent of angle $ A $ is the ratio of the length of the side opposite angle $ A $ (which is $ BC $) to the length of the side adjacent to angle $ A $ (which is $ AC $):

\[
\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{

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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y A(-5,4) C(7,4) В(7,-3) Right triangle ABC is shown in the xy-plane above. What is the value of tan A ? A) 12 B) 12 D) 3147