We have to realize that the height of a post and the horizontal distance between the posts form a right angle. Then the diagonal that joins the highest point of a post and the lowest point of the other post is the hypotenuse of a right triangle. Then we can apply the Pythagorean theorem to calculate the length of this hypotenuse.
According to the Pythagorean theorem H² = P² + D² where H is the hypotenuse (diagonal) and P the height of a post (cathetus) and D the distance between posts (cathetus).
Since we know these values, we can replace them :
H² = (48inches)² + (64inches)² = 2,304inches² + 4,096inches² = 6,400inches²
H = [tex]\sqrt{6400inches^{2}}[/tex] = 80inches
Answer : (a) 80 inches
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
