Final answer:
Using the Pythagorean theorem, the height of the TV screen with a 124 cm diagonal and a length of 98 cm is calculated to be approximately 76 cm.
Step-by-step explanation:
To find the height of the TV screen, we can use the Pythagorean theorem, which states that in a right-angled 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. In this case, the diagonal of the TV acts as the hypotenuse, and the length is one of the other sides. We will solve for the height, which is the remaining side.
Steps to calculate the height:
- Write down the Pythagorean theorem: a^2 + b^2 = c^2.
- Substitute the known values: 98^2 + b^2 = 124^2.
- Square the known values: 9604 + b^2 = 15376.
- Subtract 9604 from both sides: b^2 = 15376 - 9604.
- Calculate the difference: b^2 = 5772.
- Take the square root of both sides to find the height b: b = √5772 ≈ 76 cm.
Therefore, the height of the television screen is approximately 76 centimetres.