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Math Help - Geometry/ Triginometry

  1. #1
    Arash
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    Geometry/ Triginometry

    This is a problem im not sure of on my geometry homework. It says find the length of the apothem (distance from middle of pentagon to midpoint of 1 side) of a regular pentagon that has a perimiter of 55.

    ok, first i had to find the degrees in 1 angle so i drew lines from the middle to all midpoints and vertexes. I came up with 10 different triangles so i divided 360 by that much and I came up with 36 each angle(Not sure of this part)...Then I found the tangent of 36 and devided 5.5... (11 / 2)... by the tangent. I came up with 7.57.....this is 9th grade so i guess u guys can help me?
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  2. #2
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    Quote Originally Posted by Arash View Post
    This is a problem im not sure of on my geometry homework. It says find the length of the apothem (distance from middle of pentagon to midpoint of 1 side) of a regular pentagon that has a perimiter of 55.

    ok, first i had to find the degrees in 1 angle so i drew lines from the middle to all midpoints and vertexes. I came up with 10 different triangles so i divided 360 by that much and I came up with 36 each angle(Not sure of this part)...Then I found the tangent of 36 and devided 5.5... (11 / 2)... by the tangent. I came up with 7.57.....this is 9th grade so i guess u guys can help me?
    \tan (x)=\frac{\text{opposite}}{\text{adjacent}}

    Therefore: \text{adjacent}\cdot\tan (x)=\text{opposite}

    Then: \text{adjacent}=\frac{\text{opposite}}{\tan (x)}

    Substitute: \text{apothem}=\frac{5.5}{\tan (36)}\approx7.57010056

    So you were right!
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