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What is the area, in square feet, of an isosceles triangle whose vertex angle is 120 degrees and whose base is  20 feet long? Express your answer as a common fraction in simplest radical form.

MIRB15  Jul 7, 2017
edited by MIRB15  Jul 7, 2017
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Drawing an altitude from the apex to the base forms two 30-60-90  right triangles

 

In one of the triangles, the base  = 10   and this is the side opposite the 60° angle

 

The height of this triangle [ and of the larger triangle] will be opposite the 30° angle and wil be 10/√3  units long

 

So....the area of the biggger triangle =  (1/2)base * height =

 

(1/2) 20 * 10/√3  =  100/√3    sq units

 

Here's a pic

 

 

 

cool cool cool

CPhill  Jul 7, 2017

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