Question

A ladder 7.00 m long leans against the side of a building. If the ladder is inclined at an angle of 74.5° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?

Answer 1

x= 1.87 m

Step-by-step explanation:

We apply the concepts of trigonometry for a right triangle, where the length of the ladder is the hypotenuse of the triangle:

`cos\beta = (x)/(h)` Formula (1)

Where:

β : angle that forms x with h

x : side adjacent to the angle

h: hypotenuse of the triangle

Problem development

Look at the attached graphic

In this case, the hypotenuse is equal to the length of the ladder and x is the horizontal distance from the bottom of the ladder to the building :

h= 7.00 m

β= 74.5°

We replace data in formula (1)

`cos 74.5 = (x)/(7)`

x= 7* cos 74.5°

x= 1.87 m