Elementary Geometry For College Students, 7e
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.
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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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