Consider a triangle ABC like the one below. Suppose that b=49, a=64, and B=26°. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or". A-, C= , c = 0 0 or 0 No solution S

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.2: Angles And Their Relationships
Problem 37E: Draw a triangle with three acute angles. Construct angle bisectors for each of the three angles. On...
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**Example Problem on Triangle Calculation**

---

**Problem Statement:**

Consider a triangle \( \triangle ABC \) like the one below. Suppose that \( b = 49 \), \( a = 64 \), and \( B = 26^\circ \). (The figure is not drawn to scale.) Solve the triangle.

Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or".

**Figure Description:**

- The triangle is labeled \( ABC \). 
- Vertex \( A \) is located at one corner, with side \( c \) opposite to it.
- Vertex \( B \) is located at another corner, with side \( a \) opposite to it.
- Vertex \( C \) is located at the last corner, with side \( b \) opposite to it.

\( A = \_\_\_\_^\circ \), \( C = \_\_\_\_^\circ \), \( c = \_\_\_\_ \)

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**Calculations:**

Using the Law of Sines:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

First, we find \( A \):

\[ \sin A = \frac{a \cdot \sin B}{b} \]
\[ \sin A = \frac{64 \cdot \sin 26^\circ}{49} \]

Next, we find \( C \):

\[ C = 180^\circ - A - B \]

Finally, we find \( c \) using the Law of Sines again.

\[ c = \frac{b \cdot \sin C}{\sin B} \]

**Answer Input:**

- \( A = \_\_\_\_^\circ \)
- \( C = \_\_\_\_^\circ \)
- \( c = \_\_\_\_ \)

If more than one solution exists, utilize the "or" option. If no solution exists, indicate "No solution".

---

**Note:** Ensure to carry your intermediate computations to at least four decimal places and round your final answers to the nearest tenth.
Transcribed Image Text:**Example Problem on Triangle Calculation** --- **Problem Statement:** Consider a triangle \( \triangle ABC \) like the one below. Suppose that \( b = 49 \), \( a = 64 \), and \( B = 26^\circ \). (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or". **Figure Description:** - The triangle is labeled \( ABC \). - Vertex \( A \) is located at one corner, with side \( c \) opposite to it. - Vertex \( B \) is located at another corner, with side \( a \) opposite to it. - Vertex \( C \) is located at the last corner, with side \( b \) opposite to it. \( A = \_\_\_\_^\circ \), \( C = \_\_\_\_^\circ \), \( c = \_\_\_\_ \) --- **Calculations:** Using the Law of Sines: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] First, we find \( A \): \[ \sin A = \frac{a \cdot \sin B}{b} \] \[ \sin A = \frac{64 \cdot \sin 26^\circ}{49} \] Next, we find \( C \): \[ C = 180^\circ - A - B \] Finally, we find \( c \) using the Law of Sines again. \[ c = \frac{b \cdot \sin C}{\sin B} \] **Answer Input:** - \( A = \_\_\_\_^\circ \) - \( C = \_\_\_\_^\circ \) - \( c = \_\_\_\_ \) If more than one solution exists, utilize the "or" option. If no solution exists, indicate "No solution". --- **Note:** Ensure to carry your intermediate computations to at least four decimal places and round your final answers to the nearest tenth.
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