5) In triangle ABC, angle C is a right angle. Find the measure of angle A if side b = 195 m and side c= 255 m. Round to the nearest degree. %3D
5) In triangle ABC, angle C is a right angle. Find the measure of angle A if side b = 195 m and side c= 255 m. Round to the nearest degree. %3D
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![**5) Problem Statement:**
In triangle ABC, angle C is a right angle. Find the measure of angle A if side \(b = 195 \, \text{m}\) and side \(c = 255 \, \text{m}\). Round to the nearest degree.
**Explanation:**
To solve the problem, we use trigonometry in a right triangle. In ΔABC:
- \( \angle C = 90^\circ \)
- Side \(c\) is the hypotenuse, opposite the right angle.
- Side \(b\) is adjacent to angle \(A\).
**Using trigonometric ratios (cosine):**
\[
\cos A = \frac{\text{Adjacent side (b)}}{\text{Hypotenuse (c)}} = \frac{195}{255}
\]
Calculate \(A\) using the arccos function:
\[
A = \cos^{-1}\left(\frac{195}{255}\right)
\]
Finally, round \(A\) to the nearest degree.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35e0e75f-e8c2-4dab-b2c9-b1b559720d41%2F1692490c-2fb5-4d6d-9dd5-bd186e3beba4%2Foz11uau_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**5) Problem Statement:**
In triangle ABC, angle C is a right angle. Find the measure of angle A if side \(b = 195 \, \text{m}\) and side \(c = 255 \, \text{m}\). Round to the nearest degree.
**Explanation:**
To solve the problem, we use trigonometry in a right triangle. In ΔABC:
- \( \angle C = 90^\circ \)
- Side \(c\) is the hypotenuse, opposite the right angle.
- Side \(b\) is adjacent to angle \(A\).
**Using trigonometric ratios (cosine):**
\[
\cos A = \frac{\text{Adjacent side (b)}}{\text{Hypotenuse (c)}} = \frac{195}{255}
\]
Calculate \(A\) using the arccos function:
\[
A = \cos^{-1}\left(\frac{195}{255}\right)
\]
Finally, round \(A\) to the nearest degree.
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