An equilateral triangle has three sides of length 2m. Calculate the height of the triangle: (a)using Pythagoras rules,(b) using a trigonometrical ratios

Answer 1

hypotenuse = 2m, base = 1m

altitude or height of the triangle = square root of 2^2 -1^2 = sqr3 = about 1.732 m

height/hypotenuse = height/1 = tan60 = sqr3/1

height = sqr3 = about 1.732 m

or use the law of sines

the ratio of sinA/a = sinB/b where a and b are sides opposite angles A and B

sin60/height = sin90/2

sq3/2/height = 1/2

height = sqr3

law of cosines collapses into the Pythagorean Theorem when using a 90 degree angle

c^2 = a^2 +b^2 -2abCos90 = a^2+b^2 -2ac(0) = a^2 +b^2

2^2 = a^2 +b^2 = a^2 + 1^2

4 = a^2 +1

a^2 =4-1 =3

a =sqr3 = height

or with A=60

a^2 = c^2 +b^2 - 2abCosA

a^2 = 2^2 +1^2 - 2(2)(1)Cos60 =5 -4(1/2) = 5-2=3

a = sqr3 = height= about 1.732 m