Question
Lines x and y are parallel. If A = 104 then find the values of B and H
B = and H =
B = and H =
Answers
GPT-4o mini
To provide you with the values of B and H, I need more context about the relationships between angles A, B, and H. Generally, when two lines are parallel, various properties of angles come into play, such as corresponding angles, alternate interior angles, and consecutive interior angles.
If you can provide more information or a diagram showing how angles A, B, and H are positioned in relation to lines x and y, I can help you find the values of B and H.
If you can provide more information or a diagram showing how angles A, B, and H are positioned in relation to lines x and y, I can help you find the values of B and H.
A pythagorean triple consists of three positive integers that work with the pythagorean Theorem.
Find the missing value that be a Pythagorean Triple for a right triangle that had a length of 20 and 99.
Find the missing value that be a Pythagorean triple for a right triangle that had a length of 180 and 181
Find the missing value that be a Pythagorean Triple for a right triangle that had a length of 20 and 99.
Find the missing value that be a Pythagorean triple for a right triangle that had a length of 180 and 181
GPT-4o mini
To find the missing side in a Pythagorean triple, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side), and \( a \) and \( b \) are the lengths of the other two sides.
### 1. For the triangle with sides 20 and 99:
Assuming 99 is the hypotenuse \( c \) (this must hold, as it is longer than 20), we need to find the missing value \( a \):
\[
20^2 + a^2 = 99^2
\]
Calculating the squares:
\[
400 + a^2 = 9801
\]
Now, isolate \( a^2 \):
\[
a^2 = 9801 - 400
\]
\[
a^2 = 9401
\]
Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{9401} \approx 97
\]
So, the Pythagorean triple is \( (20, 97, 99) \).
### 2. For the triangle with sides 180 and 181:
Here, we'll assume that 181 is the hypotenuse \( c \):
\[
180^2 + a^2 = 181^2
\]
Calculating the squares:
\[
32400 + a^2 = 32761
\]
Now, isolate \( a^2 \):
\[
a^2 = 32761 - 32400
\]
\[
a^2 = 361
\]
Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{361} = 19
\]
So, the Pythagorean triple is \( (19, 180, 181) \).
### Summary:
- First triangle: \( (20, 97, 99) \)
- Second triangle: \( (19, 180, 181) \)
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side), and \( a \) and \( b \) are the lengths of the other two sides.
### 1. For the triangle with sides 20 and 99:
Assuming 99 is the hypotenuse \( c \) (this must hold, as it is longer than 20), we need to find the missing value \( a \):
\[
20^2 + a^2 = 99^2
\]
Calculating the squares:
\[
400 + a^2 = 9801
\]
Now, isolate \( a^2 \):
\[
a^2 = 9801 - 400
\]
\[
a^2 = 9401
\]
Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{9401} \approx 97
\]
So, the Pythagorean triple is \( (20, 97, 99) \).
### 2. For the triangle with sides 180 and 181:
Here, we'll assume that 181 is the hypotenuse \( c \):
\[
180^2 + a^2 = 181^2
\]
Calculating the squares:
\[
32400 + a^2 = 32761
\]
Now, isolate \( a^2 \):
\[
a^2 = 32761 - 32400
\]
\[
a^2 = 361
\]
Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{361} = 19
\]
So, the Pythagorean triple is \( (19, 180, 181) \).
### Summary:
- First triangle: \( (20, 97, 99) \)
- Second triangle: \( (19, 180, 181) \)