Question
Find the length of the unknown leg of the right triangle. Use pencil and paper. Draw the triangle on graph paper and measure to verify the answer.
37.25
12.75
(The figure is not drawn to scale.)
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Part 1
The length of the unknown leg of the right triangle is
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Answers
GPT-4o mini
To find the length of the unknown leg of a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two legs.
In your case, it looks like you have two known sides of the triangle, which are 37.25 and 12.75. You need to determine which one is the hypotenuse.
1. **Identify the hypotenuse**: The longest side is the hypotenuse. If 37.25 is the hypotenuse, the equation will be:
\[ 12.75^2 + x^2 = 37.25^2 \]
If 37.25 is not the hypotenuse and instead one of the legs, then we would be calculating it differently. But assuming it is the hypotenuse in this context:
2. **Plug in the numbers**:
\[
12.75^2 + x^2 = 37.25^2
\]
\[
162.5625 + x^2 = 1390.5625
\]
3. **Rearranging the equation** for \( x^2 \):
\[
x^2 = 1390.5625 - 162.5625
\]
\[
x^2 = 1228
\]
4. **Taking the square root** to solve for \( x \):
\[
x = \sqrt{1228}
\]
\[
x \approx 35.05
\]
So the length of the unknown leg of the right triangle is approximately **35.05**.
If you draw the triangle on graph paper and measure, you should find that the lengths you got through calculations should match close to the measurements taken from the drawing, assuming it was correctly drawn according to the dimensions given.
\[ a^2 + b^2 = c^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two legs.
In your case, it looks like you have two known sides of the triangle, which are 37.25 and 12.75. You need to determine which one is the hypotenuse.
1. **Identify the hypotenuse**: The longest side is the hypotenuse. If 37.25 is the hypotenuse, the equation will be:
\[ 12.75^2 + x^2 = 37.25^2 \]
If 37.25 is not the hypotenuse and instead one of the legs, then we would be calculating it differently. But assuming it is the hypotenuse in this context:
2. **Plug in the numbers**:
\[
12.75^2 + x^2 = 37.25^2
\]
\[
162.5625 + x^2 = 1390.5625
\]
3. **Rearranging the equation** for \( x^2 \):
\[
x^2 = 1390.5625 - 162.5625
\]
\[
x^2 = 1228
\]
4. **Taking the square root** to solve for \( x \):
\[
x = \sqrt{1228}
\]
\[
x \approx 35.05
\]
So the length of the unknown leg of the right triangle is approximately **35.05**.
If you draw the triangle on graph paper and measure, you should find that the lengths you got through calculations should match close to the measurements taken from the drawing, assuming it was correctly drawn according to the dimensions given.