**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.

Answered: Find the tangent of ZR. R 89 39 80…

Find the tangent of ZR. R 89 39 80 Simplify your answer and write it as a proper fraction, improper fraction, or whole number. tan (R) olo

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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Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

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.

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