1. A triangle with a = 5 m, b = 6 m, and the angle between the two sides is 135°. a. 10.607 m? b. 9.080 m? 2. A triangle with a = 5 m, b = 8 m, and the angle between the two sides is 27°. c. 13.499 m2 d. 20.392 m2 3. A triangle with a = 6 m, b = 7 m, and the angle between the two sides is 40°.
1. A triangle with a = 5 m, b = 6 m, and the angle between the two sides is 135°. a. 10.607 m? b. 9.080 m? 2. A triangle with a = 5 m, b = 8 m, and the angle between the two sides is 27°. c. 13.499 m2 d. 20.392 m2 3. A triangle with a = 6 m, b = 7 m, and the angle between the two sides is 40°.
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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Match the side lengths and angles to the areas of the triangles.
![**Topic: Calculating Areas of Triangles Using Side Lengths and Angles**
In this exercise, you are tasked with matching the side lengths and angles of different triangles to their respective areas. Use the formula for the area of a triangle when you know two sides and the included angle:
\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]
Here are the descriptions of four triangles with their side lengths and angles:
1. A triangle with \( a = 5 \, \text{m} \), \( b = 6 \, \text{m} \), and an included angle of \( 135^\circ \).
2. A triangle with \( a = 5 \, \text{m} \), \( b = 8 \, \text{m} \), and an included angle of \( 27^\circ \).
3. A triangle with \( a = 6 \, \text{m} \), \( b = 7 \, \text{m} \), and an included angle of \( 40^\circ \).
4. A triangle with \( a = 9 \, \text{m} \), \( b = 5 \, \text{m} \), and an included angle of \( 65^\circ \).
**Areas to Match:**
a. \( 10.607 \, \text{m}^2 \)
b. \( 9.080 \, \text{m}^2 \)
c. \( 13.499 \, \text{m}^2 \)
d. \( 20.392 \, \text{m}^2 \)
To find the correct match, calculate the area for each triangle using the given values and compare with the options provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76ebbe50-765e-48b6-ae6f-f2b4c04887d8%2F8cad7630-b4a7-48fe-b135-912c257c7d83%2Fi37bjg_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Calculating Areas of Triangles Using Side Lengths and Angles**
In this exercise, you are tasked with matching the side lengths and angles of different triangles to their respective areas. Use the formula for the area of a triangle when you know two sides and the included angle:
\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]
Here are the descriptions of four triangles with their side lengths and angles:
1. A triangle with \( a = 5 \, \text{m} \), \( b = 6 \, \text{m} \), and an included angle of \( 135^\circ \).
2. A triangle with \( a = 5 \, \text{m} \), \( b = 8 \, \text{m} \), and an included angle of \( 27^\circ \).
3. A triangle with \( a = 6 \, \text{m} \), \( b = 7 \, \text{m} \), and an included angle of \( 40^\circ \).
4. A triangle with \( a = 9 \, \text{m} \), \( b = 5 \, \text{m} \), and an included angle of \( 65^\circ \).
**Areas to Match:**
a. \( 10.607 \, \text{m}^2 \)
b. \( 9.080 \, \text{m}^2 \)
c. \( 13.499 \, \text{m}^2 \)
d. \( 20.392 \, \text{m}^2 \)
To find the correct match, calculate the area for each triangle using the given values and compare with the options provided.
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