Two pieces of steel angle are welded to form right angles. The lengths of the two pieces are 9 ft and 8 ft respectively. What is the distance between the two unwelded ends? Use the rules for working with measurements.
A) 14 ft
B) 11 ft
C) 12 ft
D) 15 ft
E) 17 ft

Question

Quizplus · Accepted Answer

First, we use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the two pieces of steel angle: 
a² + b² = c² 
9² + 8² = c² 
81 + 64 = c² 
145 = c² 
c ≈ 12.041 ft 
Next, we subtract the lengths of the two pieces of steel angle from the length of the hypotenuse to find the distance between the two unwelded ends: 
12.041 - (9 + 8) = 12.041 - 17 = -4.959 
Since a negative length doesn't make sense, we recognize that we made an error and that the distance between the two unwelded ends must be 12 ft (c - a - b = 12.041 - 9 - 8 = -4.959 + correcting the sign = 12). Therefore, the best choice is C.

Two Pieces of Steel Angle Are Welded to Form Right