An it is provided triangle has sides of size 20. Come the nearest tenth, what is the height of the it is provided triangle? Please describe what an approach you used.

You are watching: An equilateral triangle has sides of length 20


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+259 

Since every side has the same length,u got in every that the 3. Corners the same angle the 60.

Now if u split the equilateral triangle in the middle, u will obtain 2 halfs with each half having one edge of 90, one v 60(stays the very same as unsplitted) and one through 30.

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(sorry because that that terrible pic lol, but I simply went because that the an initial online draw thing on the internet)

So the center line that splits the triangle isthe heigh u desire to calculate. Since u gained a 90 angle by separating it into 2 partsu have the right to use the pythagoras to acquire the middle line.

a^2 + b^2 = c^2

b is what u desire to have, so rearrange that to:

b^2 = c^2 - a^2

Length the c is the exact same as unsplitted the 20, ais the fifty percent since u splitted the under side into 2 halfs. For this reason its 10

b^2 = 20^2 - 10^2

b^2 = 300. II ^(1/2) i cant usage latex, so thats just taking the square source 2.

Also girlfriend can try to attract thegraph to acquire the heigh,but it aint that accurate many times.


amnesia Dec 28, 2016
edited byamnesia Dec 28, 2016edited byamnesia Dec 28, 2016edited byamnesia Dec 28, 2016

4+0 Answers


 #1
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0

Area = Sqrt(3)/4 x S^2, S=Side

A=0.4330127 x 20^2

A =173.205 square units

173.205 =20 x H/2 divide both sides by 20

8.66025 =H/2 cross multiply

Height =17.3205 units.


Guest Dec 28, 2016
 #2
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+259 
+10
best Answer

Since every side has actually the same length,u got in every that the 3. Corners the exact same angle that 60.

Now if u split the it is intended triangle in the middle, u will acquire 2 halfs v each half having one angle of 90, one with 60(stays the exact same as unsplitted) and also one v 30.

*

(sorry for that dreadful pic lol, yet I simply went because that the very first online attract thing top top the internet)

So the center line that splits the triangle isthe heigh u desire to calculate. Due to the fact that u obtained a 90 angle by dividing it right into 2 partsu can use the pythagoras to obtain the center line.

a^2 + b^2 = c^2

b is what u desire to have, therefore rearrange the to:

b^2 = c^2 - a^2

Length the c is the very same as unsplitted the 20, ais the half since u splitted the under side right into 2 halfs. So its 10

b^2 = 20^2 - 10^2

b^2 = 300. II ^(1/2) i cant use latex, for this reason thats simply taking the square root 2.

Also friend can try to draw thegraph to gain the heigh,but it aint the accurate many times.


amnesia Dec 28, 2016
edited byamnesia Dec 28, 2016edited byamnesia Dec 28, 2016edited byamnesia Dec 28, 2016
 #3
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+114493 
+5

Nice pic amnesia :))


Melody Dec 28, 2016
 #4
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+34370 
+5

Another method: using Amnesia"s nice picture , you have the right to see that the now separated triangle has angles that 30 60 90

Use law of sines sin60/b = sin 30/10 ("10" comes from dividing one "20" side in fifty percent = 10)

solve because that b = 17.3205


ElectricPavlov Dec 28, 2016
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