In AQRS, the measure of S=90, OR 8.2 feet, and SO42 feet. ind the meaSure of ZR to the nearest degree.

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
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**Problem Statement:**

In triangle ΔQRS, the measure of ∠S = 90°, QR = 8.2 feet, and SQ = 4.2 feet. Find the measure of ∠R to the nearest degree.

**Diagram Explanation:**

The diagram is a right-angled triangle ΔQRS with the right angle at S. The side QR, the hypotenuse, is 8.2 feet long. The side SQ, adjacent to angle ∠R, is 4.2 feet long. 

**Diagram Details:**

- △QRS is labeled with points Q, R, and S.
- Side QR is labeled with a length of 8.2 feet.
- Side SQ is labeled with a length of 4.2 feet.
- There's a right angle symbol at point S.

**Instructions for Solution:**

To find the measure of ∠R, use trigonometric ratios. Here, use the cosine ratio because you have the lengths of the adjacent side (SQ) and the hypotenuse (QR).

- Cosine of ∠R = Adjacent side / Hypotenuse
- Cosine of ∠R = SQ / QR
- Cosine of ∠R = 4.2 / 8.2

Using a calculator, find the inverse cosine (arccos):

∠R ≈ arccos(4.2 / 8.2)

Finally, approximate the angle to the nearest degree.

**Answer Submission:**

There is an answer box for input with a submit button labeled "Submit Answer."

**Note:**
Ensure your calculator is in degree mode before computing the inverse cosine to get the measure of angle ∠R in degrees.
Transcribed Image Text:**Problem Statement:** In triangle ΔQRS, the measure of ∠S = 90°, QR = 8.2 feet, and SQ = 4.2 feet. Find the measure of ∠R to the nearest degree. **Diagram Explanation:** The diagram is a right-angled triangle ΔQRS with the right angle at S. The side QR, the hypotenuse, is 8.2 feet long. The side SQ, adjacent to angle ∠R, is 4.2 feet long. **Diagram Details:** - △QRS is labeled with points Q, R, and S. - Side QR is labeled with a length of 8.2 feet. - Side SQ is labeled with a length of 4.2 feet. - There's a right angle symbol at point S. **Instructions for Solution:** To find the measure of ∠R, use trigonometric ratios. Here, use the cosine ratio because you have the lengths of the adjacent side (SQ) and the hypotenuse (QR). - Cosine of ∠R = Adjacent side / Hypotenuse - Cosine of ∠R = SQ / QR - Cosine of ∠R = 4.2 / 8.2 Using a calculator, find the inverse cosine (arccos): ∠R ≈ arccos(4.2 / 8.2) Finally, approximate the angle to the nearest degree. **Answer Submission:** There is an answer box for input with a submit button labeled "Submit Answer." **Note:** Ensure your calculator is in degree mode before computing the inverse cosine to get the measure of angle ∠R in degrees.
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