Question

Find the exact length of the third side of a right triangle using square root. A side is missing b side = 89 and c side =80. Option 1: a = √(80² - 89²)

Option 2: a = 80 - 89
Option 3: a = 89 - 80
Option 4: a = 80 + 89

Answer 1

Using the Pythagorean theorem, the length of the missing side (a) in a right triangle with the hypotenuse (c) being 80 units and the other side (b) being 89 units is found to be 39 units when calculated correctly with the square root of the sum of squares.

Step-by-step explanation:

The student is trying to find the length of the missing side (a) in a right triangle where side b is 89 units and the hypotenuse (c) is 80 units. To solve this problem, we use the Pythagorean theorem, which in this case needs to be rearranged to solve for side a, giving us the equation a = √(c² - b²). However, there is an error in the original statement of the problem as we cannot have a hypotenuse that is shorter than one of the legs. Assuming a typo, and that side b is instead the hypotenuse (meaning b = c), the correct form of the equation would be a = √(b² - c²).

Option 1 is therefore the correct application of the theorem, but with the values swapped, leading to a = √(89² - 80²). Calculating the square root of the difference of squares gives us the exact length of side a:

a = √(7921 - 6400)
a = √(1521)
a = 39

So, the correct length of the missing side (a) is 39 units.