Question

In the accompanying diagram, a ladder leaning against a building makes an angle of 58° with level ground. If the distance from the foot of the ladder to the building is 6 feet, find, to the nearest foot, how long the ladder is?

Answer 1

The length of the ladder is 11 ft to the nearest foot

Here we want to get the length of the ladder

To get this, we have to use the appropriate trigonometric identity

To use it, we need to identify the given sides

The length of the ladder faces the right angle and it is called the hypotenuse

The side not facing the angle given and different from the hypotenuse is called the adjacent side

The appropriate trigonometric identity to use is the one that connects the hypotenuse and the adjacent

The trigonometric identity in this case is the cosine

Mathematically, we have this as;

`\begin{gathered} \cos \text{ 58 = }(6)/(h) \\ \\ h\text{ = }\frac{6}{\cos \text{ 58}} \\ h\text{ = 11 ft apprx.} \end{gathered}`