Find the exact area of this triangle. 8/3 12 [ ?]V[ ] square units Enter
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°.
Related questions
Question
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![### Find the Exact Area of This Triangle
#### Diagram Description
You are given a right triangle with the following dimensions:
- One leg is labeled with the length \(8\sqrt{3}\).
- The base is labeled with the length 12.
- The right angle is indicated by a small square.
#### Task
Calculate the exact area of the triangle. The formula for the area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
#### Solution Process
1. **Identify the base and the height:**
- Base = 12 units
- Height = \(8\sqrt{3}\) units
2. **Apply the formula for the area:**
\[
A = \frac{1}{2} \times 12 \times 8\sqrt{3}
\]
3. **Simplify the expression:**
\[
A = \frac{1}{2} \times 96\sqrt{3} = 48\sqrt{3} \text{ square units}
\]
The question reveals a formatted input for the solution, displaying a structure with:
- **[?]\(\sqrt{[\;]}\)** square units.
Here, the placeholder represents the coefficients and the square root terms in the expression for the exact area. In this case, the answer is \(48\sqrt{3}\).
#### Enter Your Answer
Students can input their calculated result in the provided field, for automatic validation and feedback.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f2c9438-5a89-4288-b691-8fe1dc913be9%2F9abf56e8-2c31-4b8e-801d-20b07875d5b3%2Fzahc9pv_processed.png&w=3840&q=75)
Transcribed Image Text:### Find the Exact Area of This Triangle
#### Diagram Description
You are given a right triangle with the following dimensions:
- One leg is labeled with the length \(8\sqrt{3}\).
- The base is labeled with the length 12.
- The right angle is indicated by a small square.
#### Task
Calculate the exact area of the triangle. The formula for the area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
#### Solution Process
1. **Identify the base and the height:**
- Base = 12 units
- Height = \(8\sqrt{3}\) units
2. **Apply the formula for the area:**
\[
A = \frac{1}{2} \times 12 \times 8\sqrt{3}
\]
3. **Simplify the expression:**
\[
A = \frac{1}{2} \times 96\sqrt{3} = 48\sqrt{3} \text{ square units}
\]
The question reveals a formatted input for the solution, displaying a structure with:
- **[?]\(\sqrt{[\;]}\)** square units.
Here, the placeholder represents the coefficients and the square root terms in the expression for the exact area. In this case, the answer is \(48\sqrt{3}\).
#### Enter Your Answer
Students can input their calculated result in the provided field, for automatic validation and feedback.
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