Answer :
To find the height of Andre's TV screen, we can use the Pythagorean theorem. The theorem applies to right triangles, and in this case, the diagonal of the TV screen acts like the hypotenuse of a right triangle, while the width and height are the two legs.
Here's how you can determine the height step-by-step:
1. Understand the Problem: We have a right triangle where one leg is the width (34 inches), and the diagonal (39 inches) is the hypotenuse. We need to find the other leg, which is the height.
2. Apply the Pythagorean Theorem: The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
[tex]\[
c^2 = a^2 + b^2
\][/tex]
In this scenario:
- [tex]\( c = 39 \)[/tex] inches (diagonal)
- [tex]\( a = 34 \)[/tex] inches (width)
- [tex]\( b \)[/tex] is the unknown height we need to find.
3. Calculate:
- Rearrange the formula to solve for the height ([tex]\( b \)[/tex]):
[tex]\[
b^2 = c^2 - a^2
\][/tex]
[tex]\[
b^2 = 39^2 - 34^2
\][/tex]
- Compute:
- [tex]\( 39^2 = 1521 \)[/tex]
- [tex]\( 34^2 = 1156 \)[/tex]
- Subtract:
[tex]\[
b^2 = 1521 - 1156 = 365
\][/tex]
- Finally, take the square root of 365 to find the height:
[tex]\[
b \approx 19.1 \text{ inches}
\][/tex]
4. Conclusion: The measurement closest to the height of Andre's TV screen is approximately 19.1 inches.
So, the closest measurement to the height of Andre's TV is 19.1 inches, option B.
Here's how you can determine the height step-by-step:
1. Understand the Problem: We have a right triangle where one leg is the width (34 inches), and the diagonal (39 inches) is the hypotenuse. We need to find the other leg, which is the height.
2. Apply the Pythagorean Theorem: The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
[tex]\[
c^2 = a^2 + b^2
\][/tex]
In this scenario:
- [tex]\( c = 39 \)[/tex] inches (diagonal)
- [tex]\( a = 34 \)[/tex] inches (width)
- [tex]\( b \)[/tex] is the unknown height we need to find.
3. Calculate:
- Rearrange the formula to solve for the height ([tex]\( b \)[/tex]):
[tex]\[
b^2 = c^2 - a^2
\][/tex]
[tex]\[
b^2 = 39^2 - 34^2
\][/tex]
- Compute:
- [tex]\( 39^2 = 1521 \)[/tex]
- [tex]\( 34^2 = 1156 \)[/tex]
- Subtract:
[tex]\[
b^2 = 1521 - 1156 = 365
\][/tex]
- Finally, take the square root of 365 to find the height:
[tex]\[
b \approx 19.1 \text{ inches}
\][/tex]
4. Conclusion: The measurement closest to the height of Andre's TV screen is approximately 19.1 inches.
So, the closest measurement to the height of Andre's TV is 19.1 inches, option B.
