Question

Tricia did such an exceptional job creating logos that she was given the task of making a banner and representing her company at a job fair. When Tricia got to the job fair, she was relieved to see there was a ladder she could use to hang the banner. While Tricia waited for someone to help her, she leaned the 12-foot ladder against the wall behind the booth. The ladder made an angle of 75 degrees with the floor. Set up and solve an equation to find how far up the wall the top ladder reaches.

Answer 1

The ladder reach up to 11.6 ft on the wall.

To solve this, we use trigonometry. We have a hypotenuse of 12ft, and we want to know the lenght of the leg opposite to the angle of 75º. The trigonometric function that relate all 3, is sine:

`\begin{gathered} \sin \theta=\frac{opposite\text{ leg}}{adjacent\text{ leg}} \\ \end{gathered}`

Using the numbers of the problem, and h is the leg we want to find:

`\begin{gathered} \sin 75º=(h)/(12ft) \\ h=\sin 75º\cdot12ft\approx11.6ft \end{gathered}`

Then the top of the ladder is at 11.6ft from the floor