Question

A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.
In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot

Answer 1

The first step in solving a problem is illustrating it just as what the picture shows. The ladder represents the hypotenuse, or the longest side of the right triangle. It measures 14 feet. The base measures 6 feet. The height of the top of the ladder from the base of the wall is denoted as x. Since this is a right triangle, the special equations for Pythagorean theorems would apply. The equation is

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the other shorter legs. Substituting the values,

14^2 = 6^2 + x^2
x^2 = 14^2 - 6^2
x^2 = 160
x = 4√10 = 12.65 feet

Answer 2

The height of the building from the top of the ladder is 12.6 ft

The situation forms a right angle triangle.

Right angle triangle:

A right angle triangle is a triangle that has one of its sides as 90 degrees.

Therefore,

The length of the ladder is the hypotenuse side.

The bottom of the ladder distance from the base of the building is the adjacent side of the triangle. Therefore,

The height of the building from the top of the ladder is the opposite sides. Therefore, using Pythagoras theorem.

c² = a² + b²

14² - 6² = b²

b² = 196 - 36

b² = 160

b = √160

b = 12.6491106407

b = 12.6 ft

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