Question
Finding the missing side of the right triangle. Round your answer to the nearest tenth. the two sides we know are 15 and 33.
Answers
GPT-4o mini
To find the missing side of a right triangle, you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (the longest side), and \( a \) and \( b \) are the other two sides.
Given the sides are 15 and 33, we need to determine whether the missing side is one of the given sides or the hypotenuse.
1. **Assuming 33 is the hypotenuse**:
\[
15^2 + b^2 = 33^2
\]
\[
225 + b^2 = 1089
\]
\[
b^2 = 1089 - 225
\]
\[
b^2 = 864
\]
\[
b = \sqrt{864} \approx 29.4
\]
2. **Assuming 15 is one of the legs and we're solving for the hypotenuse**:
\[
15^2 + 33^2 = c^2
\]
\[
225 + 1089 = c^2
\]
\[
c^2 = 1314
\]
\[
c = \sqrt{1314} \approx 36.3
\]
So, depending on which side you called the hypotenuse, the missing side is approximately **29.4** or **36.3**.
Please specify if you want to consider one case over the other for further clarity!
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (the longest side), and \( a \) and \( b \) are the other two sides.
Given the sides are 15 and 33, we need to determine whether the missing side is one of the given sides or the hypotenuse.
1. **Assuming 33 is the hypotenuse**:
\[
15^2 + b^2 = 33^2
\]
\[
225 + b^2 = 1089
\]
\[
b^2 = 1089 - 225
\]
\[
b^2 = 864
\]
\[
b = \sqrt{864} \approx 29.4
\]
2. **Assuming 15 is one of the legs and we're solving for the hypotenuse**:
\[
15^2 + 33^2 = c^2
\]
\[
225 + 1089 = c^2
\]
\[
c^2 = 1314
\]
\[
c = \sqrt{1314} \approx 36.3
\]
So, depending on which side you called the hypotenuse, the missing side is approximately **29.4** or **36.3**.
Please specify if you want to consider one case over the other for further clarity!