Determine the two missing lengths in the triangle below: 20 m A. 20-√√√3 40 3 } = C. 3 3 40√√3 X 20 3 3 3 B. a = a = m, m, } = m m D K a=20√√3 a = 40 m, m, b = 40 m b = 20-√√3 m
Determine the two missing lengths in the triangle below: 20 m A. 20-√√√3 40 3 } = C. 3 3 40√√3 X 20 3 3 3 B. a = a = m, m, } = m m D K a=20√√3 a = 40 m, m, b = 40 m b = 20-√√3 m
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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### Determine the two missing lengths in the triangle below
**Given Triangle:**
- Hypotenuse (c) = 20 m
- One side (a) = ?
- Other side (b) = ?
**Options Provided:**
#### A.
\[ a = \frac{20\sqrt{3}}{3} \, \text{m}, \quad b = \frac{40\sqrt{3}}{3} \, \text{m} \]
#### B.
\[ a = \frac{40\sqrt{3}}{3} \, \text{m}, \quad b = \frac{20\sqrt{3}}{3} \, \text{m} \]
#### C.
\[ a = 20\sqrt{3} \, \text{m}, \quad b = 40 \, \text{m} \]
**Student's Selection:**
- C. \[ a = 20\sqrt{3} \, \text{m}, \quad b = 40 \, \text{m} \] (marked incorrect with a red cross)
**Note:**
- In the provided right triangle diagram, the angle opposite to side 'a' and adjacent to side 'b' is indicated.
When dealing with right triangles and given one side along with the hypotenuse, the Pythagorean theorem is often used to find the missing sides. The relationships are as follows:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse.
---
In the given options:
- Option A gives values for sides 'a' and 'b' both involving \(\sqrt{3}\) divided by 3.
- Option B similarly provides 'a' and 'b' with switched values compared to Option A.
- Option C directly gives the values of 'a' and 'b' without a denominator.
In this context, for a right triangle with specific given side lengths and evaluating each option should correctly satisfy the Pythagorean theorem to identify the valid lengths.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5a061b4-0108-4a51-81fc-44207999c893%2F3da53e0c-6ec1-4ca0-8ebb-91265f63e3ec%2Ff9b6aee_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Determine the two missing lengths in the triangle below
**Given Triangle:**
- Hypotenuse (c) = 20 m
- One side (a) = ?
- Other side (b) = ?
**Options Provided:**
#### A.
\[ a = \frac{20\sqrt{3}}{3} \, \text{m}, \quad b = \frac{40\sqrt{3}}{3} \, \text{m} \]
#### B.
\[ a = \frac{40\sqrt{3}}{3} \, \text{m}, \quad b = \frac{20\sqrt{3}}{3} \, \text{m} \]
#### C.
\[ a = 20\sqrt{3} \, \text{m}, \quad b = 40 \, \text{m} \]
**Student's Selection:**
- C. \[ a = 20\sqrt{3} \, \text{m}, \quad b = 40 \, \text{m} \] (marked incorrect with a red cross)
**Note:**
- In the provided right triangle diagram, the angle opposite to side 'a' and adjacent to side 'b' is indicated.
When dealing with right triangles and given one side along with the hypotenuse, the Pythagorean theorem is often used to find the missing sides. The relationships are as follows:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse.
---
In the given options:
- Option A gives values for sides 'a' and 'b' both involving \(\sqrt{3}\) divided by 3.
- Option B similarly provides 'a' and 'b' with switched values compared to Option A.
- Option C directly gives the values of 'a' and 'b' without a denominator.
In this context, for a right triangle with specific given side lengths and evaluating each option should correctly satisfy the Pythagorean theorem to identify the valid lengths.
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