Find the area of each of the following triangles. Give exact values whenever possible. Otherwise, round answers to the nearest hundredth. Note: Figures may not be drawn to scale.
DO NOT USE A CALCULATOR. there is only ONE right answer choice
Transcribed Image Text:**Problem 7.2.14**
Select the correct answer from the options given:
A. \(\frac{35 \sqrt{3}}{4} \, \text{ft}^2\)
B. \(\frac{35 \sqrt{2}}{4} \, \text{ft}^2\)
C. \(\frac{35 \sqrt{3}}{2} \, \text{ft}^2\)
D. \(\frac{35}{4} \, \text{ft}^2\)
E. \(\frac{35 \sqrt{2}}{2} \, \text{ft}^2\)
Transcribed Image Text:### Transcription of Diagram
**Problem 14 Description:**
This diagram represents a geometric configuration involving three points, D, E, and F, which form a triangle.
- **Line Segment DE:**
- Length: 7 feet
- Point D is on the left, and point E is to the right of D.
- **Line Segment EF:**
- Length: 5 feet
- Connects point E to point F.
- **Angle DEF:**
- Measures 135 degrees.
- This is the angle formed between line segments DE and EF.
The diagram illustrates a situation where two side lengths and the included angle of a triangle (DEF) are given. This setup is useful for applying geometric principles such as the Law of Cosines to find missing side lengths or angles.
Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).
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