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
Related questions
Question
![**Title: Solving a 30/60/90 Triangle**
**Question:**
The hypotenuse of a 30/60/90 triangle is 20 - what is the length of the longer leg?
**Options:**
- 10
- 12
- 16
- 10√3
**Explanation:**
To solve this problem, we need to understand the properties of a 30/60/90 triangle. In this special right triangle:
- The hypotenuse is twice the length of the shorter leg.
- The longer leg is the shorter leg times √3.
Given that the hypotenuse is 20, we can find the shorter leg as follows:
\[ \text{Shorter leg} = \frac{\text{Hypotenuse}}{2} = \frac{20}{2} = 10 \]
Next, we use the property of the triangle to find the longer leg:
\[ \text{Longer Leg} = \text{Shorter leg} \times \sqrt{3} = 10 \times \sqrt{3} = 10\sqrt{3} \]
Thus, the answer is 10√3.
**Answer:**
- 10
- 12
- 16
- **10√3** (correct answer)
This type of question helps in understanding and practicing key geometrical properties that are essential in various fields of study such as mathematics, engineering, and architecture.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb294f3d7-c37e-4d19-872e-5bb2e2baac27%2F94b89ea1-8da3-40b5-9d45-392465891bf3%2Frmsxoy5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Solving a 30/60/90 Triangle**
**Question:**
The hypotenuse of a 30/60/90 triangle is 20 - what is the length of the longer leg?
**Options:**
- 10
- 12
- 16
- 10√3
**Explanation:**
To solve this problem, we need to understand the properties of a 30/60/90 triangle. In this special right triangle:
- The hypotenuse is twice the length of the shorter leg.
- The longer leg is the shorter leg times √3.
Given that the hypotenuse is 20, we can find the shorter leg as follows:
\[ \text{Shorter leg} = \frac{\text{Hypotenuse}}{2} = \frac{20}{2} = 10 \]
Next, we use the property of the triangle to find the longer leg:
\[ \text{Longer Leg} = \text{Shorter leg} \times \sqrt{3} = 10 \times \sqrt{3} = 10\sqrt{3} \]
Thus, the answer is 10√3.
**Answer:**
- 10
- 12
- 16
- **10√3** (correct answer)
This type of question helps in understanding and practicing key geometrical properties that are essential in various fields of study such as mathematics, engineering, and architecture.
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