+0  
 
0
69
1
avatar

A parallelogram has perimeter 40 and altitudes of length 4 and 7. Find the sine of the smaller vertex angle.

 May 13, 2020
 #1
avatar+21953 
+1

The parallelogram has a shorter side (let's call it 'x') and a longer side (which is '20-x').

 

The altitude of length 4 goes to the longer side. Using the area of a parallelogram to be its side times its altitude,

the area of the parallelogram is 4·(20 - x).

 

Using the shorter side (x) and its altitude (7) to find the area, we get 7·x.

 

Therefore:  4·(20 - x)  =  7·x 

                      80 - 4x  =  7x

                             80  =  11x

                               x  =  80/11

 

To find the sine of the smaller vertex angle:  sine(angle)  =  4 / (80/11)  =  44/80  =  11/20 

 May 13, 2020

12 Online Users

avatar
avatar