Question

Raymond was riding a zip-cable from the top of a viewing post. The cable is 65 yards long. The viewing post is 52 yards high and forms a right angle with the ground, as shown in the picture below.

Answer 1

B. 33 yards

Explanation:

Let x represent the height of the viewing post, y represent the how far the base of the viewing post is from the end of the cable, and z represent the length of the cable. Now, use the Pythagorean theorem.

x2 + y2 = z2

(44 yd)2 + y2 = (55 yd)2

1,936 yd2 + y2 = 3,025 yd2

y2 = 1,089 yd2

y = 33 yd

So, the end of the cable is 33 yards from the base of the viewing post.

Answer 2

In order to figure out the horizontal distance Raymond travels using his zip cable, we may simply apply Pythagoras theorem which is, for a right triangle:
hypotenuse² = base² + height²
base = √(hypotenuse² - height²)
base = √(65² - 52²)
base = 39 yards
Raymond will travel a horizontal distance of 39 yards.