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
How did I solve for q
![### Trigonometry Worksheet
#### Problem 4:
Given the right-angled triangle below, find the length of the side \( q \).
##### Diagram:
- A right-angled triangle is shown.
- The hypotenuse is labeled as 12 cm.
- The height (the perpendicular side) is labeled as \( q \) cm.
- The base (the horizontal side) has not been labeled with a value.
The triangle is denoted with the right angle at vertex \( B \).
To solve for \( q \), use the Pythagorean Theorem, which states:
\[ c^2 = a^2 + b^2 \]
- Where \( c \) is the hypotenuse.
- \( a \) and \( b \) are the other two sides of the triangle.
In this diagram:
- \( c = 12 \) cm
- Let \( a = q \) cm and \( b \) be the base.
Thus:
\[ c^2 = q^2 + b^2 \]
\[ (12 \text{ cm})^2 = q^2 + b^2 \]
\[ 144 \text{ cm}^2 = q^2 + b^2 \]
To solve for \( q \), more information is needed, specifically the length of the base \( b \). If the base \( b \) were known, this equation could be solved by substituting \( b \) and solving for \( q \).
If no additional information is provided:
\[ q = \sqrt{144 \text{ cm}^2 - b^2} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37df3d5a-a285-4454-8f45-9a850ef8be3f%2F0e22cef2-ff49-4922-abea-fc7fe924e1d2%2F8d85k0g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometry Worksheet
#### Problem 4:
Given the right-angled triangle below, find the length of the side \( q \).
##### Diagram:
- A right-angled triangle is shown.
- The hypotenuse is labeled as 12 cm.
- The height (the perpendicular side) is labeled as \( q \) cm.
- The base (the horizontal side) has not been labeled with a value.
The triangle is denoted with the right angle at vertex \( B \).
To solve for \( q \), use the Pythagorean Theorem, which states:
\[ c^2 = a^2 + b^2 \]
- Where \( c \) is the hypotenuse.
- \( a \) and \( b \) are the other two sides of the triangle.
In this diagram:
- \( c = 12 \) cm
- Let \( a = q \) cm and \( b \) be the base.
Thus:
\[ c^2 = q^2 + b^2 \]
\[ (12 \text{ cm})^2 = q^2 + b^2 \]
\[ 144 \text{ cm}^2 = q^2 + b^2 \]
To solve for \( q \), more information is needed, specifically the length of the base \( b \). If the base \( b \) were known, this equation could be solved by substituting \( b \) and solving for \( q \).
If no additional information is provided:
\[ q = \sqrt{144 \text{ cm}^2 - b^2} \]
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