Question
A carpenter is measuring a cabinet to ensure the sides create a right angle.
M80704_DHW_001A.png
Determine whether the triangle is a right triangle.
M80704_DHW_001A.png
Determine whether the triangle is a right triangle.
Answers
GPT-4o mini
To determine if the triangle in the cabinet is a right triangle, you can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
If we denote the lengths of the sides of the triangle as \( a \), \( b \), and \( c \) (where \( c \) is the hypotenuse), the theorem can be expressed as:
\[
c^2 = a^2 + b^2
\]
To use this theorem:
1. Measure the lengths of the three sides of the triangle.
2. Identify the longest side, which should be the hypotenuse (let's call this side \( c \)).
3. Square the lengths of all three sides.
4. Check if the sum of the squares of the two shorter sides equals the square of the longest side.
If the equation holds true, then the triangle is a right triangle. If it does not, then the triangle is not a right triangle.
If you provide specific measurements, I can help you with the calculations!
If we denote the lengths of the sides of the triangle as \( a \), \( b \), and \( c \) (where \( c \) is the hypotenuse), the theorem can be expressed as:
\[
c^2 = a^2 + b^2
\]
To use this theorem:
1. Measure the lengths of the three sides of the triangle.
2. Identify the longest side, which should be the hypotenuse (let's call this side \( c \)).
3. Square the lengths of all three sides.
4. Check if the sum of the squares of the two shorter sides equals the square of the longest side.
If the equation holds true, then the triangle is a right triangle. If it does not, then the triangle is not a right triangle.
If you provide specific measurements, I can help you with the calculations!