Question

At the circus, an acrobat is standing on a platform that is 27 feet from the ground when he sees a peanut on the ground below. How far is the peanut away from the base of the platform if the angle of elevation from the peanut to top of the acrobat's platform is 25°?​

Answer 1

The peanut is 12.59 feet away from the base of the platform.

Explanation:

When solving these equations, we can first start out by noticing that this requires a trigonometry function.

There are three types : cos, sin, and tan. (cosine, sin, and tangent)

Cos is for finding and dealing with the adjacent and the hypotenuse.

Sin is for finding and dealing with the opposite and the hypotenuse.

Tan is for finding and dealing with the opposite and the adjacent.

The opposite is the bottom base, to the peanut.

The adjacent is the height from the bottom base, to the top.

The hypotenuse is the top, to the peanut.

27 feet would be the adjacent.

Since we don't know bottom base to the peanut, we would call this x. (opposite)

*Side note* : The degrees is always in between the adjacent and hypotenuse.

For this, we need the length between the peanut and the bottom base. This would be the adjacent and the opposite. Meaning we're using tangent. The equation for tangent is :

tan (degrees) = opposite/adjacent

So, now we simply put in the data.

tan 25 = x/27

We can now, first get x alone by multipling both sides by 27.

27 * tan 25 = x

Plug this into a scientific calculator :

27 * tan 25

We the answer to be 12.59

The peanut is 12.59 feet away from the base of the platform