The formula that relates the length of a ladder, l, that leans against a wall with distance d from the base of the wall and the height h that the ladder reaches up the wall is l = startroot d squared + h squared endroot. what height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base of a wall?
11.5 feet
13.1 feet
14.6 feet
15.4 feet

The height of the ladder = 14.6 feet

Given formula is

where l = Length of the ladder.

d = Distance from the base of wall

h = Vertical height of the ladder  

According to the Pythagoras Theorem (Figure attached )

Given that

Length of the ladder= 15 ft

Distance from the base of wall = 3.5 ft

So the vertical height of the ladder is given by the equation (1)

.....(1)

h=

h= 14.6 ft

So the height of the ladder = 14.6 feet

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The correct answer is C. 14.6 feet

Step-by-step explanation:

Information given to solve the case:

Length of the ladder = 15 feet

Distance from the base of the wall = 3.5 feet

Using the Pythagorean theorem for finding the height, because this is a right triangle:

h² = Length of the ladder ² - Distance from the base of the wall ²

h² = 15 ²  - 3.5 ²

h² = 225  - 12.25

h² = 212.75

h = √ 212.75

h = 14.59

h = 14.6 feet (Rounding to one decimal place)

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