Final answer:
To find 'a' in a right triangle when c = 85 and b = 53, we use the Pythagorean theorem and solve the equation a² + b² = c². After substituting the values, simplifying the equation, and solving for 'a', we get a ≈ 66.5 (rounded to the nearest tenth).
Step-by-step explanation:
To find the value of 'a', one of the legs of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of one leg added to the square of the length of the other leg is equal to the square of the length of the hypotenuse.
In this case, we are given the lengths of the hypotenuse (c = 85) and one of the legs (b = 53). To find the length of the other leg 'a', we can rearrange the equation: a² + b² = c², and solve for 'a'.
First, substitute the given values: a² + 53² = 85². Then, simplify the equation: a² + 2809 = 7225. Finally, solve for 'a' by subtracting 2809 from both sides of the equation and taking the square root of both sides: a = √4416 ≈ 66.5 (rounded to the nearest tenth).