SOLUTION: To the nearest tenth what is the altitude of an equilateral triangle whose sides measure 43 centimeters?

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Question 1089694: To the nearest tenth what is the altitude of an equilateral triangle whose sides measure 43 centimeters?
Found 3 solutions by ikleyn, jim_thompson5910, MathTherapy:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
the altitude h = ,  where a is the side length.

You do the rest.



Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start by drawing out an equilateral triangle ABC. Each point is a vertex of the triangle.
Then plot another point D such that it is the midpoint of one of the sides.
I made point D the midpoint of segment AB.
In this case, the altitude is the segment from point C to point D.
Let's call the altitude h for now (h for height)
This is what the drawing should look like



Note how D splits AB into two equal halves.

We have these properties:

AD = DB
AD = 21.5, DB = 21.5 (43/2 = 21.5)
AD+DB = 21.5+21.5 = 43 = AB

----------------------------------------------

Using that drawing above as reference, and focusing on triangle CDB, let's find what h must equal.

Because triangle CDB is a right triangle, we can use the pythagorean theorem

a = 21.5
b = h
c = 43

Start with the pythagorean theorem

Plug in the given values

Square the terms

Subtract 462.25 from both sides

Simplify

Take the square root of both sides

Compute the square root (use a calculator)

Round to the nearest tenth

The altitude is roughly 37.2 cm


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
To the nearest tenth what is the altitude of an equilateral triangle whose sides measure 43 centimeters?
An altitude drawn from a vertex to the 3rd side of an equilateral triangle creates two 30-60-90 SPECIAL triangles. 

In THIS case, each of these 2 special triangles will have as its hypotenuse, 43 cm. With the hypotenuse known, the LONGER LEG (opposite the LARGER of the 2 ACUTE angles, or opposite the 60o angle) 

will have a value of:  

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