Question

A ladder 7.50 m long leans against the side of a building. If the ladder is inclined at an angle of 67.0° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?_____ m

Answer 1

The horizontal distance is x m, this distance is adjacent to the angle of 67°. The ladder forms a rectangle triangle, therefore the ladder length is the hypotenuse, 7.50 m. The trigonometric function that relates these items is cosine

$cos(67\degree)=\frac{x\text{ m}}{7.50\text{ m}}\text{ }$

In order to find the value of m

$cos(67\degree)\times7.50=x\text{ }\Rightarrow x=2.93\text{ m}$

The horizontal distance from the bottom of the ladder to the building is 2.93 m.