Question

In a playground a slide that is 12 m long runs over a horizontal distance of 8 meters along the ground .find the angle and slide makes the ground

Answer 1

We are given the following information

The main goal is to solve for x. First, we identify the the slide corresponds to the hypotenuse of the triangle. The horiziontal distance is the adjacent side with respect angle x. To find angle x, we should use a trigonometric ratio that relates the adjacent side and the hypotenuse. This ratio would be the cosine. Recall that

`\cos (\text{angle)}=\frac{length\text{ adjacent side }}{length\text{ of the hypotenuse}}`

In this case, we have

`\cos (x)=\frac{\text{length of adjacent side}}{length\text{ of the hypotenuse}}=(8)/(12)`

To find the value of x, we apply the arccos function both sides, we get

`x=\arccos ((8)/(12))\approx48.1896\text{ degress}`

So, rounded to the nearest degree, x is approximately 48°.