Use the triangle at the right. Find the missing length to the nearest tenth of a unit. 10. a = 11 in., c = 42 in. 11. b = 14 cm, c = 22 cm 12. a = 17 ft, c = 45 ft b.
Use the triangle at the right. Find the missing length to the nearest tenth of a unit. 10. a = 11 in., c = 42 in. 11. b = 14 cm, c = 22 cm 12. a = 17 ft, c = 45 ft b.
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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![**Using the Pythagorean Theorem to Find Missing Lengths**
To solve for missing side lengths in right triangles, use the Pythagorean Theorem:
\[a^2 + b^2 = c^2\]
Here \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.
**Problem Set**
**Use the triangle diagram at the right for reference. Find the missing length to the nearest tenth of a unit.**
**Given:**
- \[a\]
- \[b\]
**Find the missing side length \(c\) if known sides are \(a\) and \(b\). Otherwise, find the unknown side as specified.**
**Problems:**
10. \[a = 11 \text{ in., } c = 42 \text{ in.}\]
- \[b \approx\]
11. \[b = 14 \text{ cm, } c = 22 \text{ cm}\]
- \[a \approx\]
12. \[a = 17 \text{ ft, } c = 45 \text{ ft}\]
- \[b \approx\]
**Triangle Diagram Explanation:**
This right triangle depicts:
- \(a\) as one of the perpendicular legs,
- \(b\) as the other perpendicular leg, and
- \(c\) as the hypotenuse (the side opposite the right angle).
To find the missing side:
1. Plug the known values into the Pythagorean Theorem:
- If \(a\) or \(b\) is missing, rearrange to solve for the missing variable.
- Square the known sides.
- Subtract the square of the known side from the hypotenuse squared to find the missing side squared.
2. Take the square root of the result to find the missing side length to the nearest tenth.
**Example Calculation:**
**For Problem 10:**
- Given: \(a = 11 \text{ in., } c = 42 \text{ in.}\)
- Find \(b\).
\[11^2 + b^2 = 42^2\]
\[121 + b^2 = 1764\]
\[b^2 = 1764 - 121\]
\[b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6cd6a4e-6666-4ce9-a995-c6ee7f0343e2%2F4dd140b4-5e70-4d52-befc-2e39560bef89%2Fh2zfsag_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using the Pythagorean Theorem to Find Missing Lengths**
To solve for missing side lengths in right triangles, use the Pythagorean Theorem:
\[a^2 + b^2 = c^2\]
Here \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.
**Problem Set**
**Use the triangle diagram at the right for reference. Find the missing length to the nearest tenth of a unit.**
**Given:**
- \[a\]
- \[b\]
**Find the missing side length \(c\) if known sides are \(a\) and \(b\). Otherwise, find the unknown side as specified.**
**Problems:**
10. \[a = 11 \text{ in., } c = 42 \text{ in.}\]
- \[b \approx\]
11. \[b = 14 \text{ cm, } c = 22 \text{ cm}\]
- \[a \approx\]
12. \[a = 17 \text{ ft, } c = 45 \text{ ft}\]
- \[b \approx\]
**Triangle Diagram Explanation:**
This right triangle depicts:
- \(a\) as one of the perpendicular legs,
- \(b\) as the other perpendicular leg, and
- \(c\) as the hypotenuse (the side opposite the right angle).
To find the missing side:
1. Plug the known values into the Pythagorean Theorem:
- If \(a\) or \(b\) is missing, rearrange to solve for the missing variable.
- Square the known sides.
- Subtract the square of the known side from the hypotenuse squared to find the missing side squared.
2. Take the square root of the result to find the missing side length to the nearest tenth.
**Example Calculation:**
**For Problem 10:**
- Given: \(a = 11 \text{ in., } c = 42 \text{ in.}\)
- Find \(b\).
\[11^2 + b^2 = 42^2\]
\[121 + b^2 = 1764\]
\[b^2 = 1764 - 121\]
\[b
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