Use the Pythagorean Theorem to determine the missing side of the following right triangle rounded to the nearest tenth unit.

Answer

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is a ^2 + b ^2 = c ^2 , where 'a' and 'b' are the lengths of the legs of the right triangle and 'c' is the length of the hypotenuse. In the given right triangle, the lengths of the two legs are x and 35, and the length of the hypotenuse is 45. According to the Pythagorean Theorem, we have: x ^2 + 35 ^2 = 45 ^2 Calculate the squares: x ^2 + 1225 = 2025 Subtract 1225 from both sides of the equation: x ^2 = 2025 - 1225 x ^2 = 800 Take the square root of both sides to find the value of x: x = \sqrt{800} Calculate the square root of 800: x \approx 28.28427 We are asked to round the answer to the nearest tenth unit. The digit in the tenths place is 2, and the digit in the hundredths place is 8. Since 8 is greater than or equal to 5, we round up the tenths digit. x \approx 28.3 The missing side of the right triangle, rounded to the nearest tenth unit, is 28.3 units.