Using the figure below, find the measure of angle A. Round your answer to the nearest degree. Drawing is not to scale. 52 in (A 112 in 65 in A. 146° B. 124° 65° D. 56°
Using the figure below, find the measure of angle A. Round your answer to the nearest degree. Drawing is not to scale. 52 in (A 112 in 65 in A. 146° B. 124° 65° D. 56°
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Problem 18**
**Question:** Using the figure below, find the measure of angle \(A\). Round your answer to the nearest degree. Drawing is not to scale.
**Figure Description:** The figure is a triangle with the following sides:
- Opposite side to angle \(A\) = 52 in
- Adjacent side to angle \(A\) = 65 in
- Hypotenuse = 112 in
**Answer Choices:**
- A. \(146^\circ\)
- B. \(124^\circ\)
- C. \(65^\circ\) (crossed out with a red "X")
- D. \(56^\circ\)
**Explanation:**
To solve this problem, you need to apply the law of cosines. The law of cosines states:
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
where:
- \( c \) is the length of the side opposite the angle \( C \),
- \( a \) and \( b \) are the lengths of the other two sides.
From the given figure:
\[ c = 112\; \text{in}, \; a = 52\; \text{in}, \; b = 65\; \text{in} \]
Plugging in these values:
\[ 112^2 = 52^2 + 65^2 - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
Calculate the values for each term:
- \( 112^2 = 12544 \)
- \( 52^2 = 2704 \)
- \( 65^2 = 4225 \)
Then:
\[ 12544 = 2704 + 4225 - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
\[ 12544 = 6929 - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
Solve for \( \cos(A) \):
\[ 12544 - 6929 = - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
\[ 5615 = - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
\[ 5615 = -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4904ad93-6dcc-43fa-9122-8f69394907f2%2Fafa4d957-809d-4234-9d4a-d4d162c333df%2Fn6nicdf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 18**
**Question:** Using the figure below, find the measure of angle \(A\). Round your answer to the nearest degree. Drawing is not to scale.
**Figure Description:** The figure is a triangle with the following sides:
- Opposite side to angle \(A\) = 52 in
- Adjacent side to angle \(A\) = 65 in
- Hypotenuse = 112 in
**Answer Choices:**
- A. \(146^\circ\)
- B. \(124^\circ\)
- C. \(65^\circ\) (crossed out with a red "X")
- D. \(56^\circ\)
**Explanation:**
To solve this problem, you need to apply the law of cosines. The law of cosines states:
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
where:
- \( c \) is the length of the side opposite the angle \( C \),
- \( a \) and \( b \) are the lengths of the other two sides.
From the given figure:
\[ c = 112\; \text{in}, \; a = 52\; \text{in}, \; b = 65\; \text{in} \]
Plugging in these values:
\[ 112^2 = 52^2 + 65^2 - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
Calculate the values for each term:
- \( 112^2 = 12544 \)
- \( 52^2 = 2704 \)
- \( 65^2 = 4225 \)
Then:
\[ 12544 = 2704 + 4225 - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
\[ 12544 = 6929 - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
Solve for \( \cos(A) \):
\[ 12544 - 6929 = - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
\[ 5615 = - 2 \cdot 52 \cdot 65 \cdot \cos(A) \]
\[ 5615 = -
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