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

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°?

thugiang · Answer

Answer:   The peanut is  12.59 feet  away from the base of the platform.   Step-by-step 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

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