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
Related questions
Question
What is the tan(x) for each
![**Question 11**
**What is the tan(x) for each triangle?** * [2 points]
The image shows two right-angled triangles.
**Triangle on the left:**
- Angle \(X\)
- Side \(A\) (adjacent to angle \(X\))
- Side \(B\) (opposite to angle \(X\))
- Hypotenuse \(C\)
- Right angle (\(90^\circ\))
**Triangle on the right:**
- Angle \(X\)
- Side \(D\) (adjacent to angle \(X\))
- Side \(E\) (opposite to angle \(X\))
- Hypotenuse \(F\)
- Right angle (\(90^\circ\))
**Explanation of `tan(x)`:**
The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.
\[ \tan(X) = \frac{\text{opposite side}}{\text{adjacent side}} \]
For the triangle on the left:
\[ \tan(X) = \frac{B}{A} \]
For the triangle on the right:
\[ \tan(X) = \frac{E}{D} \]
To find the exact values of \( \tan(X) \) for each triangle, substitute the lengths of the sides into the respective formulas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56c0d7e7-dec0-442e-807e-93dee8ab6b46%2F184c64ff-83a4-4a63-ac5f-c3cb82ccb17a%2Fys866la_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 11**
**What is the tan(x) for each triangle?** * [2 points]
The image shows two right-angled triangles.
**Triangle on the left:**
- Angle \(X\)
- Side \(A\) (adjacent to angle \(X\))
- Side \(B\) (opposite to angle \(X\))
- Hypotenuse \(C\)
- Right angle (\(90^\circ\))
**Triangle on the right:**
- Angle \(X\)
- Side \(D\) (adjacent to angle \(X\))
- Side \(E\) (opposite to angle \(X\))
- Hypotenuse \(F\)
- Right angle (\(90^\circ\))
**Explanation of `tan(x)`:**
The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.
\[ \tan(X) = \frac{\text{opposite side}}{\text{adjacent side}} \]
For the triangle on the left:
\[ \tan(X) = \frac{B}{A} \]
For the triangle on the right:
\[ \tan(X) = \frac{E}{D} \]
To find the exact values of \( \tan(X) \) for each triangle, substitute the lengths of the sides into the respective formulas.
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