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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Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
Find the value of the missing angle X. Round your answer to the nearest tenth.
![In the image, there is a right triangle with one angle explicitly marked as a right angle (90 degrees) at the bottom right corner. The sides of the triangle are labeled with the following lengths:
- The length of the hypotenuse (the side opposite the right angle) is given as 30 units.
- The length of the base (horizontal side) of the triangle is given as 18 units.
- The third side, the height (vertical side) of the triangle, is labeled as \( x \).
To find the value of \( x \), we can use the Pythagorean theorem, which states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the lengths of the legs of the triangle, and \( c \) is the length of the hypotenuse.
In this case, the base 18 units and the height \( x \) are the legs of the triangle, and 30 units is the hypotenuse. Substituting these values into the Pythagorean theorem gives:
\[ 18^2 + x^2 = 30^2 \]
\[ 324 + x^2 = 900 \]
Subtracting 324 from both sides:
\[ x^2 = 576 \]
Taking the square root of both sides, we get:
\[ x = 24 \]
Therefore, the length of the height \( x \) is 24 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff66317fc-ed86-4f22-9308-86904c21cc6d%2Ffda0d9ca-52d6-4ea6-b784-896e83a107ff%2Ftrwgblp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the image, there is a right triangle with one angle explicitly marked as a right angle (90 degrees) at the bottom right corner. The sides of the triangle are labeled with the following lengths:
- The length of the hypotenuse (the side opposite the right angle) is given as 30 units.
- The length of the base (horizontal side) of the triangle is given as 18 units.
- The third side, the height (vertical side) of the triangle, is labeled as \( x \).
To find the value of \( x \), we can use the Pythagorean theorem, which states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the lengths of the legs of the triangle, and \( c \) is the length of the hypotenuse.
In this case, the base 18 units and the height \( x \) are the legs of the triangle, and 30 units is the hypotenuse. Substituting these values into the Pythagorean theorem gives:
\[ 18^2 + x^2 = 30^2 \]
\[ 324 + x^2 = 900 \]
Subtracting 324 from both sides:
\[ x^2 = 576 \]
Taking the square root of both sides, we get:
\[ x = 24 \]
Therefore, the length of the height \( x \) is 24 units.
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