Answer:
a) 13.86 feet up the wall.
b) 14.83 feet up the wall.
Explanation:
In both cases, we use the Pythagoras Theorem to solve the question.
a. If he places the base of the ladder 8 feet from the wall, how high up the wall will the ladder reach? Draw a diagram to support your work.
The length of the ladder is the hypothenuse. In this case, the base is 8, and we have to find the height h. The problem is represented by the diagram below.
Applying the Pythagoras Theorem:
8² + h² = 16²
64 + h² = 256
h² = 256 - 64
h² = 192
h = square root of 192
h = 13.86
13.86 feet up the wall.
b. If he places the base of the ladder 6 feet from the wall, how high up the wall will the ladder reach? Draw a diagram to support your work.
Similar to previous question, just the base is 6.
6² + h² = 16²
36 + h² = 256
h² = 256 - 36
h² = 220
h = square root of 220
h = 14.83
14.83 feet up the wall.