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
![**Find the Tangent of ∠R**
In the given right triangle ΔQRS:
- The hypotenuse QR measures 89 units.
- The side QS (adjacent to ∠R) measures 80 units.
- The side RS (opposite to ∠R) measures 39 units.
To find the tangent of ∠R, we use the tangent function, which is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
So,
\[ \tan(\angle R) = \frac{RS}{QS} \]
Substituting the given values:
\[ \tan(\angle R) = \frac{39}{80} \]
Therefore, the tangent of ∠R is:
\[ \tan(R) = \frac{39}{80} \]
**Instructions for Answer Submission:**
- Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
- Input the simplified value in the designated answer box.
You may select the appropriate format using the provided calculator tool.
Example answer:
\[ \tan(R) = \frac{39}{80} \]
Note: The diagram provided shows a right triangle ΔQRS with a right angle at ∠S. This visual aid helps in understanding the relationships between the sides and angles in the triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa89e63f8-66db-4f4d-a2d5-5c1b9146f99d%2Ff863f126-ab14-4db6-92ad-6b0333024d15%2Fat78do_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the Tangent of ∠R**
In the given right triangle ΔQRS:
- The hypotenuse QR measures 89 units.
- The side QS (adjacent to ∠R) measures 80 units.
- The side RS (opposite to ∠R) measures 39 units.
To find the tangent of ∠R, we use the tangent function, which is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
So,
\[ \tan(\angle R) = \frac{RS}{QS} \]
Substituting the given values:
\[ \tan(\angle R) = \frac{39}{80} \]
Therefore, the tangent of ∠R is:
\[ \tan(R) = \frac{39}{80} \]
**Instructions for Answer Submission:**
- Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
- Input the simplified value in the designated answer box.
You may select the appropriate format using the provided calculator tool.
Example answer:
\[ \tan(R) = \frac{39}{80} \]
Note: The diagram provided shows a right triangle ΔQRS with a right angle at ∠S. This visual aid helps in understanding the relationships between the sides and angles in the triangle.
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