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If the vertex angle of an isosceles triangle has a measure of 60 and the length of each leg is 18, find the length of the altitude drawn to the base.

Rose98  Jul 9, 2014

Best Answer 

 #1
avatar+996 
+10

Ah, lovely, an easy one. Equilateral triangle. After this one I'm eating dinner x3

 

60 - 60 - 60 means all sides are equal. Altitude splits this one perfectly in half as well, and makes a 30 - 60 - 90 triangle. 30 - 60 - 90 means x - x(squareroot(3)) - 2x.

 

2x is equal to one of the original legs, which is 18. x is equal to the split leg, or 9. x(squareroot(3)) equals the altitude, and since x = 9, x(squareroot(3)) = 9(squareroot(3))

 

9(squareroot(3)) is your answer.

GoldenLeaf  Jul 9, 2014
 #1
avatar+996 
+10
Best Answer

Ah, lovely, an easy one. Equilateral triangle. After this one I'm eating dinner x3

 

60 - 60 - 60 means all sides are equal. Altitude splits this one perfectly in half as well, and makes a 30 - 60 - 90 triangle. 30 - 60 - 90 means x - x(squareroot(3)) - 2x.

 

2x is equal to one of the original legs, which is 18. x is equal to the split leg, or 9. x(squareroot(3)) equals the altitude, and since x = 9, x(squareroot(3)) = 9(squareroot(3))

 

9(squareroot(3)) is your answer.

GoldenLeaf  Jul 9, 2014
 #2
avatar+4150 
+5

Are you going to eat the cookie on your avatar?

zegroes  Jul 9, 2014
 #3
avatar+88898 
+5

Very nicely done, GL...I was gonna' use trig, but your way is definitely more elegant.....

3 pts. and a thumb from me!!!

 

 

CPhill  Jul 9, 2014

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