Question

5 lisas parents purchase a flat screen television. the screen measures 45 inches on the diagonal. the base of the screen is 36 inches long. what is the height, in inches, of the television screen? write your answer in the space provided. in. 6 a helicopter rises vertically 3 kilometers and then

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle (where the diagonal of the screen is the hypotenuse \(c\), the base is \(a\) and the height is \(b\)) is \(a^{2}+b^{2}=c^{2}\). Let the base \(a = 36\) inches and the diagonal \(c=45\) inches. We need to find the height \(b\). So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 36\) and \(c = 45\) into the formula \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=45^{2}-36^{2}\). Calculate \(45^{2}=2025\) and \(36^{2}=1296\). So, \(b^{2}=2025 - 1296=729\).

Step3: Find \(b\)

Take the square root of \(b^{2}\). Since \(b>0\) (height cannot be negative), \(b=\sqrt{729}=27\).

Answer:

\(27\)