Question
One of the legs of a right triangle measures 16 cm and the other leg measures 10 cm . Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Ask by Harrington Maxwell. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The hypotenuse is approximately 18.9 cm.
Solution
To find the measure of the hypotenuse of a right triangle when the lengths of the two legs are known, you can use the **Pythagorean Theorem**, which states:
\[ c = \sqrt{a^2 + b^2} \]
where:
- \( c \) is the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two legs.
**Given:**
- One leg (\( a \)) = 16 cm
- Other leg (\( b \)) = 10 cm
**Calculation:**
1. **Square both legs:**
\[
a^2 = 16^2 = 256
\]
\[
b^2 = 10^2 = 100
\]
2. **Sum the squares:**
\[
a^2 + b^2 = 256 + 100 = 356
\]
3. **Take the square root to find the hypotenuse:**
\[
c = \sqrt{356} \approx 18.86796226 \text{ cm}
\]
4. **Round to the nearest tenth:**
\[
c \approx 18.9 \text{ cm}
\]
**Answer:**
The hypotenuse measures approximately 18.9 centimeters.
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Simplify this solution Mind Expander
To find the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse. Plugging in the values: \(16^2 + 10^2 = c^2\) This gives us: \(256 + 100 = c^2\) So, \(356 = c^2\) Taking the square root of both sides: \(c \approx 18.9\) cm (rounded to the nearest tenth). Now you have the measure of the hypotenuse as approximately 18.9 cm!
