Final answer:
To find the missing side length using the Pythagorean theorem, you calculate the hypotenuse (c) as the square root of the sum of the squares of the other two sides (a and b). For the given values, the hypotenuse of the first triangle is approximately 22.1, the length of the second side (b) of the second triangle is about 5.7, and the hypotenuse of the third triangle is around 10.6, all rounded to the nearest tenth.
Step-by-step explanation:
To use the Pythagorean theorem for finding the missing side length of a right triangle, you follow the established relationship: a² + b² = c². Considering the values given in the question (a=7, b=21), the hypotenuse (c) would be calculated as:
For the first triangle:
c = √(7² + 21²)
c = √(49 + 441)
c = √490
c ≈ 22.1 (rounded to the nearest tenth).
For the second triangle:
b = √(c² - a²)
b = √(7² - 4²)
b = √(49 - 16)
b = √33
b ≈ 5.7 (rounded to the nearest tenth).
For the third triangle:
c = √(a² + (2√3)²)
c = √(8² + (4√3))
c = √(64 + 48)
c = √112
c ≈ 10.6 (rounded to the nearest tenth).