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) About Me  (Show Source):
You can put this solution on YOUR website!
.
the altitude h = a%2A%28sqrt%283%29%2F2%29,  where a is the side length.

You do the rest.



Answer by jim_thompson5910(35256) About Me  (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

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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

a%5E2+%2B+b%5E2+=+c%5E2 Start with the pythagorean theorem

%2821.5%29%5E2+%2B+h%5E2+=+%2843%29%5E2 Plug in the given values

462.25+%2B+h%5E2+=+1849 Square the terms

462.25+%2B+h%5E2+-+462.25+=+1849+-+462.25 Subtract 462.25 from both sides

h%5E2+=+1386.75 Simplify

sqrt%28h%5E2%29+=+sqrt%281386.75%29 Take the square root of both sides

h+=+37.2390923627309 Compute the square root (use a calculator)

h+=+37.2 Round to the nearest tenth

The altitude is roughly 37.2 cm


Answer by MathTherapy(10552) About Me  (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: