Use the Law of Sines to find the indicated side x. (Assume a = 155. Round your answer to one decimal place.) X = a 102° - 28° A B
Use the Law of Sines to find the indicated side x. (Assume a = 155. Round your answer to one decimal place.) X = a 102° - 28° A B
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
![**Problem Statement:**
Use the Law of Sines to find the indicated side \( x \). (Assume \( a = 155 \). Round your answer to one decimal place.)
**Diagram Explanation:**
The diagram shows a triangle \( \triangle ABC \), where:
- Angle \( A \) is \( 102^\circ \).
- Angle \( B \) is \( 28^\circ \).
- Side \( a \) opposite angle \( A \) is labeled as 155.
- Side \( x \) is opposite angle \( B \) and is the value to be determined.
**Solution Using the Law of Sines:**
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Therefore:
\[
\frac{a}{\sin A} = \frac{x}{\sin B}
\]
Substitute the known values:
\[
\frac{155}{\sin 102^\circ} = \frac{x}{\sin 28^\circ}
\]
Solve for \( x \):
\[
x = \frac{155 \cdot \sin 28^\circ}{\sin 102^\circ}
\]
Calculate the value of \( x \), rounding to one decimal place.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ae03bb8-ec3d-406c-93d2-922fad9dd684%2Ffb644e65-5cdf-4d31-a880-1b97ea9b6170%2F4dj26kv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Use the Law of Sines to find the indicated side \( x \). (Assume \( a = 155 \). Round your answer to one decimal place.)
**Diagram Explanation:**
The diagram shows a triangle \( \triangle ABC \), where:
- Angle \( A \) is \( 102^\circ \).
- Angle \( B \) is \( 28^\circ \).
- Side \( a \) opposite angle \( A \) is labeled as 155.
- Side \( x \) is opposite angle \( B \) and is the value to be determined.
**Solution Using the Law of Sines:**
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Therefore:
\[
\frac{a}{\sin A} = \frac{x}{\sin B}
\]
Substitute the known values:
\[
\frac{155}{\sin 102^\circ} = \frac{x}{\sin 28^\circ}
\]
Solve for \( x \):
\[
x = \frac{155 \cdot \sin 28^\circ}{\sin 102^\circ}
\]
Calculate the value of \( x \), rounding to one decimal place.
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