ketch the triangle. LA = 30°, LC = 65°, b = 14 C A 65 14 30° В 30° 14 C 65° 30 14 14 30° A А 65°
ketch the triangle. LA = 30°, LC = 65°, b = 14 C A 65 14 30° В 30° 14 C 65° 30 14 14 30° A А 65°
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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![**Triangle Sketching Exercise**
**Problem:**
Sketch the triangle.
\(\angle A = 30^\circ\), \(\angle C = 65^\circ\), \(b = 14\)
**Diagrams:**
1. The first triangle is labeled \(ABC\), with:
- \(\angle B = 65^\circ\)
- \(\angle C = 30^\circ\)
- Side \(AC = 14\)
2. The second triangle is rotated, labeled \(ABC\), with:
- \(\angle A = 65^\circ\)
- \(\angle C = 30^\circ\)
- Side \(BC = 14\)
3. The third triangle is labeled \(ABC\), with:
- \(\angle B = 30^\circ\)
- \(\angle C = 65^\circ\)
- Side \(AB = 14\)
4. The fourth triangle is confirmed as correct:
- \(\angle A = 30^\circ\)
- \(\angle C = 65^\circ\)
- Side \(AB = 14\)
**Task:**
Solve the triangle using the Law of Sines. (Round side lengths to one decimal place.)
- \(a =\)
- \(c =\)
- \(\angle B =\)
**Guidance:**
To solve the triangle, apply the Law of Sines:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Calculate the missing side lengths and angle \(B\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F410204a0-8764-4473-a9c2-14bad68c17f5%2F5d2e414b-5ca3-4b13-93eb-a04cf7d9f7ed%2Fl7gdizb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Triangle Sketching Exercise**
**Problem:**
Sketch the triangle.
\(\angle A = 30^\circ\), \(\angle C = 65^\circ\), \(b = 14\)
**Diagrams:**
1. The first triangle is labeled \(ABC\), with:
- \(\angle B = 65^\circ\)
- \(\angle C = 30^\circ\)
- Side \(AC = 14\)
2. The second triangle is rotated, labeled \(ABC\), with:
- \(\angle A = 65^\circ\)
- \(\angle C = 30^\circ\)
- Side \(BC = 14\)
3. The third triangle is labeled \(ABC\), with:
- \(\angle B = 30^\circ\)
- \(\angle C = 65^\circ\)
- Side \(AB = 14\)
4. The fourth triangle is confirmed as correct:
- \(\angle A = 30^\circ\)
- \(\angle C = 65^\circ\)
- Side \(AB = 14\)
**Task:**
Solve the triangle using the Law of Sines. (Round side lengths to one decimal place.)
- \(a =\)
- \(c =\)
- \(\angle B =\)
**Guidance:**
To solve the triangle, apply the Law of Sines:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Calculate the missing side lengths and angle \(B\).
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