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The altitude to the hypotenuse of a triangle with angles of 30 and 60 degrees is 3 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.

 Dec 23, 2020
 #1
avatar+114325 
+1

We can split the base into two parts....m  and n

 

tan 30° =  3 /m

 

sqrt (3) / 3 =  3/m

 

m = 3 / ( sqrt (3) / 3)

 

m = 9 / sqrt (3)  =   3 sqrt (3)

 

 

tan 60° = 3 / n

 

sqrt (3)  = 3 / n

 

n  = 3 /sqrt (3)  =  sqrt (3)

 

So....area  =

 

(1/2) base length * height  =

 

(1/2) (m + n) * height  =

 

(1/2)  (3sqrt (3)  + sqrt (3) )* 3  =

 

(1/2) ( 4 sqrt (3) )  * 3   =

 

2sqrt (3) * 3  = 

 

6sqrt (3)  (square units)

 

 

cool cool cool

 Dec 23, 2020
edited by CPhill  Dec 23, 2020
 #2
avatar+859 
+1

A = [3*(3 / tan60º + 3 / tan30º)] / 2 = 6√3

 Dec 24, 2020

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