1. ## 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?

2. Originally Posted by Arash
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?
$\displaystyle \tan (x)=\frac{\text{opposite}}{\text{adjacent}}$

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

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

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

So you were right!