Problem:
We are given a right triangle with the following dimensions:
- One leg (adjacent to the right angle) is 14 units.
- The other leg (opposite to the right angle) is 11.5 units.
- We need to determine the length of the hypotenuse \( AB \).
The formula for the hypotenuse in a right triangle is given by the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
where:
- \( c \) is the hypotenuse,
- \( a \) and \( b \) are the lengths of the two legs.
Step-by-Step Solution:
1.
Identify the given values:
- \( a = 14 \) (one leg),
- \( b = 11.5 \) (the other leg).
2.
Apply the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
Substitute the given values:
\[
c^2 = 14^2 + 11.5^2
\]
3.
Calculate \( 14^2 \):
\[
14^2 = 196
\]
4.
Calculate \( 11.5^2 \):
\[
11.5^2 = 11.5 \times 11.5 = 132.25
\]
5.
Add the squares of the legs:
\[
c^2 = 196 + 132.25 = 328.25
\]
6.
Solve for \( c \) by taking the square root of both sides:
\[
c = \sqrt{328.25}
\]
7.
Calculate the square root:
\[
c \approx 18.12
\]
8.
Round the result to the nearest tenth:
\[
c \approx 18.1
\]
Final Answer:
\[
\boxed{18.1}
\]
Parent Tip: Review the logic above to help your child master the concept of 10th grade geometry worksheets.
