Question

Bob wants to build a slide for his 5-year-old son, Bobby. He has read that any slide that is steeper than 35 degrees from the bottom of the slide is too dangerous. The platform for the slide is 4 feet high and he has 7 feet of ground allotted for the slide.

Using inverse trig ratios, does Bob have enough room to safely build the slide. SHOW the calculations you will enter into the calculator. SHOW the result. Tell if the slide is safe. If it is 35 degrees or less, from the bottom of the slide, it is!

Answer 1

We are given height of a slide and aloted ground:
a = 4ft
b = 7ft

To find out the angle we need to use trigonometry. Here we have right-angle triangle. In that case we have lengths of two sides but not hypothenuze. We can use tangens function to find angle:
$tan \alpha = \frac {opposite}{adjacent}$

We need inverse tangens function to find angle:
$\alpha =tan^{-1} ( \frac{opposite}{adjacent} ) \\ \alpha =tan^{-1} ( \frac{4}{7} ) \\ \alpha =29.75°$

The angle is less than 35 degrees so it is safe to build it.