Question
A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. If the rope is 28 feet long. how tall is the mast? Round to the nearest tenth of a foot.
Ask by Elliott Conner. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The mast is approximately 20.6 feet tall.
Solution
To determine the height of the mast, we can use the Pythagorean theorem. Here's a step-by-step breakdown:
1. **Identify the Right Triangle Components:**
- **Horizontal distance from the mast (base):** 19 feet
- **Length of the rope (hypotenuse):** 28 feet
- **Height of the mast (vertical side):** \( h \) feet
2. **Apply the Pythagorean Theorem:**
\[
h^2 + 19^2 = 28^2
\]
3. **Calculate the Squares:**
\[
h^2 + 361 = 784
\]
4. **Solve for \( h^2 \):**
\[
h^2 = 784 - 361 = 423
\]
5. **Find \( h \):**
\[
h = \sqrt{423} \approx 20.566 \text{ feet}
\]
6. **Round to the Nearest Tenth:**
\[
h \approx 20.6 \text{ feet}
\]
**Therefore, the height of the mast is approximately 20.6 feet.**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the height of the mast, you can visualize the situation as a right triangle where the height of the mast is one leg (let's call it 'h'), the distance from the mast to the anchor point where the rope is tied is the other leg (19 feet), and the length of the rope acts as the hypotenuse (28 feet). Using the Pythagorean theorem (a² + b² = c²), we can set it up as follows: h² + 19² = 28². This simplifies to h² + 361 = 784. Subtracting 361 from both sides gives us h² = 423. Taking the square root of 423, we find h ≈ 20.6 feet. Therefore, the mast is approximately 20.6 feet tall when rounded to the nearest tenth. Happy sailing!
