Find the height of an equilateral triangle with sides 12 cm long. Leave your answer in radical form.?

Question

Thanks for any help.

Answer 1

Hi,

An equilateral triangle is really easy. Realize that all its sides are the same and all its angles are 60 degrees. If you drop an altitude down through the center of the triangle, it splits the triangle into 2 30-60-90 degree triangles. They have sides with a pattern - if the side across from the 30 degree angle is "s" long, then the side across from the 60 degree angle is "s"radical 3 and the side across from the right angle has a length of "2s". When you drop that altitude down through the triangle it splits the 60 degrees at the top into 2 30 degree angles. It also splits the bottom side in half. That means the bottom side of 12 cm is split into 6 cm on the left and 6 cm on the right. Notice that that 6 is the value of "s", across from the 30 degree angle at the top. The side of the equilateral triangle is the hypotenuse of the 30-60-90 triangle so "2s" is 12. The third side has the "s radical 3" as its length, so the altitude is 6radical 3. This is the same as 6 sqrt(3).

Your other answer gave you 2 radical 27 as the answer. That radical could still be simplified to make the answer 6 radical 3.

I hope that helps!! :-)

Answer 2

The height of an equilateral triangle bisects the base, so h = √(12^2 - 6^2) = √6^2(4 - 1) = 6√3

Answer 3

One way of solving it:
Sides are 12 cm each - will form 2 right angled traingles so
use pythagorean ( a² + b² = c²)
Base of traingle is 12 cm so half is 6 cm - a line from the base up to the vertex would make a 90° angle and then pythagorean can be used.

a² + 6² = c²
a² + 36 = 12²
a² + 36 = 144
a² = 144 - 36
a² = 108
a = √108
a = 10.39 cm

Answer 4

you can figure this out because of the 30-60-90 triangle and the altitude would be one leg of the right triangle and the other leg would be half the side lenght. and the hypotenuse would be equal to the side lenght so you can use that to fighure out that the altitude is 12 squared muinus 6 squared which equals the squrare root 108 which is 6 times root 3. So 6 times root 3 is your answer.

Answer 5

*First, cut the triangle in half vertically. This will give you two, equal 90-degree triangles. Use the pythagorean theorem to solve for the height (in this case, it'll be a).

a^2 + b^2 = c^2
a^2 + (6)^2 = (12)^2
a^2 = 108
a = 10.392 (the square root of 108)

Answer 6

By Phytagoras' Theorem, the height is sqrt (12^2 - 6 ^2) = sqrt (144 - 36) = sqrt (108) = sqrt (3*36) = 6 * sqrt (3)

(sqrt stands for square root)

Answer 7

the top varieties a 30-60-ninety degree triangle with the backside. for this reason the top is factor/2 * sqrt(3)= 7sqrt(3). you will possibly desire to remember all of the particular triangle formula. it truly is going to shop you lots time on exams and homework.

Answer 8

yes leave it in radical form, the answer is 2 radical 27

Answer 9

h = a sqrt(3)/2

h = 12 * sqrt(3)/2
h = 6sqrt(3)

ANS : 6sqrt(3)cm