Geometry: find altitude of equi. triangle given side lengths

[henryvmhs]

Question: What is the length of an altitude of an equilateral triangle with side lengths of 4 times the square root of 3?

 

[jwpaine]

Re: Geometry

Question: What is the length of an altitude of an equilateral triangle with side lengths of 4 times the square root of 3?

equilateral triangle = all sides of same length & each angle is 60 degrees

Cut the triangle in half so that you have a smaller triangle composed of three sides: (1/2)(base), height, and \(\displaystyle 4\sqrt{3}\)
Now use right-angle trig methods to find the height:

The angle where the (1/2)(base), height, and \(\displaystyle 4\sqrt{3}\) meet is 60 degrees.

You can now say that Sin(60) = \(\displaystyle \frac{h}{4\sqrt{3}}\)

Solve for h

Cheers,
John

 

[soroban]

Re: Geometry

Hello, henryvmhs!

What is the length of an altitude of an equilateral triangle with side lengths of \(\displaystyle 4\sqrt{3}\) ?

= . . . . . . . . . . . . . .\(\displaystyle *\)
- . . . . . . . . . . . . \(\displaystyle *\;*\;*\)
- . . . . . . . . . . . \(\displaystyle *\;\;\;*\;\;\;*\)
- . . . . . . . . . . \(\displaystyle *\;\;\;\;\;*\;\;\;\;\;*\;\;4\sqrt{3}\)
- . . . . . . . . . \(\displaystyle *\;\;\;\;\;\;\;*\text{h}\,\,\,\;\;\;*\)
- . . . . . . . . \(\displaystyle *\;\;\;\;\;\;\;\;\;*\;\;\;\;\;\;\;\;\;*\)
. . . . . . . . \(\displaystyle *\;\;\;\;\;\;\;\;\;\;\;*\;\;\;\;\;\;\;\;\;\;\;*\)
. . . . . . . \(\displaystyle *\;*\;*\;*\;*\;*\;*\;*\;*\;*\)
. . . . . . . . . . . . . . . . . \(\displaystyle 2\sqrt{3}\)

. . . . .. . Use Pythagorus!