bike Owen is building a triangular Jump. It will be 2' high and ramp. Draw and have a 6' Label a diagram illustrating his ramp How long must the base be EXACTLY and rounded to the nearest tenth.
bike Owen is building a triangular Jump. It will be 2' high and ramp. Draw and have a 6' Label a diagram illustrating his ramp How long must the base be EXACTLY and rounded to the nearest tenth.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.3: Properties Of Numbers
Problem 51PPS
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![**Problem Description:**
Owen is building a triangular bike jump. It will be 2 feet high and have a 6-foot ramp. Draw and label a diagram illustrating his ramp. How long must the base be EXACTLY and rounded to the nearest tenth.
**Detailed Explanation for Educational Website:**
Owen is constructing a triangular bike jump, which includes the following dimensions:
- **Height:** 2 feet
- **Ramp Length (Hypotenuse):** 6 feet
To find the length of the base of the triangular ramp, we can use the Pythagorean Theorem, which is expressed as:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) is one leg of the triangle (the height in this case, which is 2 feet),
- \(b\) is the other leg of the triangle (the base, which we need to find), and
- \(c\) is the hypotenuse of the triangle (the ramp length, which is 6 feet).
First, plug in the known values:
\[ (2)^2 + b^2 = (6)^2 \]
\[ 4 + b^2 = 36 \]
Next, isolate \(b^2\):
\[ b^2 = 36 - 4 \]
\[ b^2 = 32 \]
Finally, take the square root of both sides to solve for \(b\):
\[ b = \sqrt{32} \]
\[ b \approx 5.656 \]
Thus, the exact length of the base is \(\sqrt{32}\), and when rounded to the nearest tenth, it is approximately 5.7 feet.
**Diagram:**
- Draw a right triangle.
- Label the vertical leg \(2 \, \text{feet}\).
- Label the hypotenuse \(6 \, \text{feet}\).
- Label the base approximately \(5.7 \, \text{feet}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94589190-d7d8-41be-9c6e-d2d51b756765%2Fcad6c812-4ba8-4718-851d-97d45e02dab0%2Fehqh8fh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
Owen is building a triangular bike jump. It will be 2 feet high and have a 6-foot ramp. Draw and label a diagram illustrating his ramp. How long must the base be EXACTLY and rounded to the nearest tenth.
**Detailed Explanation for Educational Website:**
Owen is constructing a triangular bike jump, which includes the following dimensions:
- **Height:** 2 feet
- **Ramp Length (Hypotenuse):** 6 feet
To find the length of the base of the triangular ramp, we can use the Pythagorean Theorem, which is expressed as:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) is one leg of the triangle (the height in this case, which is 2 feet),
- \(b\) is the other leg of the triangle (the base, which we need to find), and
- \(c\) is the hypotenuse of the triangle (the ramp length, which is 6 feet).
First, plug in the known values:
\[ (2)^2 + b^2 = (6)^2 \]
\[ 4 + b^2 = 36 \]
Next, isolate \(b^2\):
\[ b^2 = 36 - 4 \]
\[ b^2 = 32 \]
Finally, take the square root of both sides to solve for \(b\):
\[ b = \sqrt{32} \]
\[ b \approx 5.656 \]
Thus, the exact length of the base is \(\sqrt{32}\), and when rounded to the nearest tenth, it is approximately 5.7 feet.
**Diagram:**
- Draw a right triangle.
- Label the vertical leg \(2 \, \text{feet}\).
- Label the hypotenuse \(6 \, \text{feet}\).
- Label the base approximately \(5.7 \, \text{feet}\).
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