In an equilateral triangle with side 'a',prove that altitude =√3by2/a?
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Where a is the side of the equilateral triangle.
Now let's prove that using some trigonometric I
As you can see in the above image all the angles in an equilateral triangle are 60° and all the sides are congruent, which is represented as a.
Now, area of triangle= 1/2 ×base × height
Let's find out the base and height.
Base= BC = a
Angle ABD= 60°
Sin B = opposite side/hypotenuse
Sin60= AD/AB
√3/2= height/a [ since, sin60= √3/2]
Height= √3/2× a
Now we have both height and base,so let's substitute it in the formula.
Area of equilateral triangle= 1/2× base× height
= 1/2× a× √3/2× a
= √3/4 ×a^2
So, it is proved.
Now let's prove that using some trigonometric I
As you can see in the above image all the angles in an equilateral triangle are 60° and all the sides are congruent, which is represented as a.
Now, area of triangle= 1/2 ×base × height
Let's find out the base and height.
Base= BC = a
Angle ABD= 60°
Sin B = opposite side/hypotenuse
Sin60= AD/AB
√3/2= height/a [ since, sin60= √3/2]
Height= √3/2× a
Now we have both height and base,so let's substitute it in the formula.
Area of equilateral triangle= 1/2× base× height
= 1/2× a× √3/2× a
= √3/4 ×a^2
So, it is proved.
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