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Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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### Finding Angles in a Triangle
**Jun 18, 6:54:46 PM**
#### Watch help video
In \( \Delta HIJ \), \( j = 1.9 \) inches, \( h = 3.4 \) inches and \( \angle I = 161^\circ \). Find \( \angle J \), to the nearest 10th of a degree.
---
**Answer:**
\[ \boxed{} \]
*Submit Answer*
*attempt 1 out of 2*
---
**Explanation:**
In this problem, you are given certain measurements and an angle of a triangle and asked to find one of the other angles.
- \( \Delta HIJ \) represents a triangle with vertices \(H\), \(I\), and \(J\).
- Side \( j \) (opposite to vertex \( J \)) is 1.9 inches long.
- Side \( h \) (opposite to vertex \( H \)) is 3.4 inches long.
- The angle at vertex \( I \) is \( 161^\circ \).
To find \( \angle J \):
1. Apply the Law of Sines which states:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Given that:
\[
\frac{j}{\sin J} = \frac{h}{\sin H} = \frac{i}{\sin I}
\]
2. Rearrange and solve for \(\sin J\):
\[
\sin J = \frac{j \cdot \sin I}{h}
\]
3. Compute \(\angle J\) by taking the inverse sine (\(\sin^{-1}\)) of the result obtained.
Finally, ensure that the angle is rounded to the nearest 10th of a degree before submitting your answer.](https://content.bartleby.com/qna-images/question/8fb42b59-2abc-4047-983a-bfb263ef58de/3e25cd61-1611-4644-9cd5-9c5c87c1b879/rvl1lw_thumbnail.jpeg)
Transcribed Image Text:---
### Finding Angles in a Triangle
**Jun 18, 6:54:46 PM**
#### Watch help video
In \( \Delta HIJ \), \( j = 1.9 \) inches, \( h = 3.4 \) inches and \( \angle I = 161^\circ \). Find \( \angle J \), to the nearest 10th of a degree.
---
**Answer:**
\[ \boxed{} \]
*Submit Answer*
*attempt 1 out of 2*
---
**Explanation:**
In this problem, you are given certain measurements and an angle of a triangle and asked to find one of the other angles.
- \( \Delta HIJ \) represents a triangle with vertices \(H\), \(I\), and \(J\).
- Side \( j \) (opposite to vertex \( J \)) is 1.9 inches long.
- Side \( h \) (opposite to vertex \( H \)) is 3.4 inches long.
- The angle at vertex \( I \) is \( 161^\circ \).
To find \( \angle J \):
1. Apply the Law of Sines which states:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Given that:
\[
\frac{j}{\sin J} = \frac{h}{\sin H} = \frac{i}{\sin I}
\]
2. Rearrange and solve for \(\sin J\):
\[
\sin J = \frac{j \cdot \sin I}{h}
\]
3. Compute \(\angle J\) by taking the inverse sine (\(\sin^{-1}\)) of the result obtained.
Finally, ensure that the angle is rounded to the nearest 10th of a degree before submitting your answer.
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