Solve A ABC. Round your answer to the nearest hundredth (two digits to the right of the decimal point) if necessary. A 65 C= 5 b B C = degrees a 2 (Just type a number in each box.
Solve A ABC. Round your answer to the nearest hundredth (two digits to the right of the decimal point) if necessary. A 65 C= 5 b B C = degrees a 2 (Just type a number in each box.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Solving Triangle ABC
**Problem Statement:**
Solve △ABC. Round your answer to the nearest hundredth (two digits to the right of the decimal point) if necessary.
**Triangle Diagram Explanation:**
The triangle depicted is a right-angled triangle with the following details:
- Angle ∠BAC = 65°
- Side c (opposite angle B) = 5 units
- The right angle is at ∠B.
**Unknowns to Find:**
- Angle ∠C
- Side a (adjacent to angle A)
- Side b (opposite angle A)
**Formulas to Use:**
1. **Finding Angle ∠C:**
∠C = 90° - ∠A
∠C = 90° - 65°
∠C = 25°
2. **Using Trigonometric Ratios to Find Sides a and b:**
- **Side a (adjacent to ∠A):**
\[
\cos(65^\circ) = \frac{a}{c}
\]
\[
a = c \cdot \cos(65^\circ)
\]
\[
a = 5 \cdot \cos(65^\circ) \approx 2.11
\]
- **Side b (opposite to ∠A):**
\[
\sin(65^\circ) = \frac{b}{c}
\]
\[
b = c \cdot \sin(65^\circ)
\]
\[
b = 5 \cdot \sin(65^\circ) \approx 4.53
\]
### Fill in the Blanks:
- Angle ∠C ≈ 25° (degrees)
- Side a ≈ 2.11
- Side b ≈ 4.53
(Just type a number in each box.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e6bee82-3f3d-4249-8519-dfc591a10d22%2F96f51dfa-a3b6-489f-8728-bc5d2223f720%2F20ayvvc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Triangle ABC
**Problem Statement:**
Solve △ABC. Round your answer to the nearest hundredth (two digits to the right of the decimal point) if necessary.
**Triangle Diagram Explanation:**
The triangle depicted is a right-angled triangle with the following details:
- Angle ∠BAC = 65°
- Side c (opposite angle B) = 5 units
- The right angle is at ∠B.
**Unknowns to Find:**
- Angle ∠C
- Side a (adjacent to angle A)
- Side b (opposite angle A)
**Formulas to Use:**
1. **Finding Angle ∠C:**
∠C = 90° - ∠A
∠C = 90° - 65°
∠C = 25°
2. **Using Trigonometric Ratios to Find Sides a and b:**
- **Side a (adjacent to ∠A):**
\[
\cos(65^\circ) = \frac{a}{c}
\]
\[
a = c \cdot \cos(65^\circ)
\]
\[
a = 5 \cdot \cos(65^\circ) \approx 2.11
\]
- **Side b (opposite to ∠A):**
\[
\sin(65^\circ) = \frac{b}{c}
\]
\[
b = c \cdot \sin(65^\circ)
\]
\[
b = 5 \cdot \sin(65^\circ) \approx 4.53
\]
### Fill in the Blanks:
- Angle ∠C ≈ 25° (degrees)
- Side a ≈ 2.11
- Side b ≈ 4.53
(Just type a number in each box.)
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