act Math assist » Geometry » plane Geometry » triangles » Equilateral triangle » exactly how to discover the size of the next of an it is provided triangle

The height of an it is provided triangle is . Discover the perimeter.    Explanation:

From the given information, us can draw the complying with picture: Since this is an it is intended triangle, all 3 of that angles will be congruent. All three of its sides will additionally be congruent.

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The dotted line, representing the height, bisects not only the base of the triangle but additionally the apical angle. This method that the two smaller right triangles produced by the dotted line have actually bases the are half the side length of the equilateral triangle with apical angle steps of  , to deal with for the length of one of the it is intended triangle"s sides.

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2. You can use trig attributes to deal with for the length of one of the it is provided triangle"s sides.

Using trig functions, we can use as our edge of interest, with the size and the hypotenuse being our an enig side.

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Going back to SOH CAH TOA, we have the right to determine the we will certainly be making use of sine because we have actually the information available for the side opposite ("O") of our angle of interest and are searching for the hypotenuse ("H"). This way we will be utilizing the "SOH" part of SOH CAH TOA—sine. Substituting in the problem"s values, we have the right to solve because that the length of the hypotenuse of one of the two smaller sized triangles, i m sorry is the length of one side the the it is intended triangle:    Remember the the difficulty asks for the triangle"s perimeter. That method that we need to multiply the length of one of its edge by three to discover the last answer: